tag:blogger.com,1999:blog-625730140494703392011-12-23T13:49:30.767-05:00Fractal JourneyA visual exploration of fractal geometryOrson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.comBlogger62125tag:blogger.com,1999:blog-62573014049470339.post-7422377910698605792011-12-09T21:16:00.001-05:002011-12-13T20:53:04.839-05:002011-12-13T20:53:04.839-05:00In memory of Benoit Mandelbrot<br />
<iframe allowfullscreen="" frameborder="0" height="360" src="http://www.youtube.com/embed/KLamH6Dl90w?hd=1" width="640"></iframe>
<br />
<br />
<br />
A tribute to <a href="http://en.wikipedia.org/wiki/Benoit_Mandelbrot">Benoit Mandelbrot</a> (20 November 1924 - 14 October 2010) - a maverick of academia.<br />
<br />
Thanks to <a href="http://itunes.apple.com/us/album/suburban-films/id305508932">Dark Flow</a> for the music "Groggy Sunrise".<br />
<br />
<b>Planetarium proposal </b><br />
Ken Hawthorn (at the <a href="http://planetarium.deanza.edu/">Fujitsu Planetarium</a>,
De-Anza college in Cupertino, California) gave me the idea of projecting a Mandelbrot zoom in a planetarium. Inspired by Dr. Mandelbrot's death
last year, I attempted to create a high definition rendering of a Mandelbrot zoom
that could be appreciated by those who have never seen it before and could be
projected in a Planetarium setting. Synchronization of zoom events against appropriate music is one key element. Planetarium operators are welcome to
contact me to use this material gratis via Creative Commons license.<br />
<br />
<b>Coordinates</b><br />
Mandelbrot<br />
Final zoom location:<br />
real=<span style="font-family: "Courier New",Courier,monospace;">0.0134388705</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3201212902</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8364919004</span><br />
<span style="font-family: "Courier New",Courier,monospace;">0196868675</span><br />
<span style="font-family: "Courier New",Courier,monospace;">2857331456</span><br />
<span style="font-family: "Courier New",Courier,monospace;">5492885548</span><br />
<span style="font-family: "Courier New",Courier,monospace;">699</span><br />
Img=<span style="font-family: "Courier New",Courier,monospace;">0.6556142187</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6946506225</span><br />
<span style="font-family: "Courier New",Courier,monospace;">1320027664</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6174666912</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9597586478</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6403994151</span><br />
<span style="font-family: "Courier New",Courier,monospace;">735</span><br />
magn=<span style="font-family: "Courier New",Courier,monospace;">6.5139268e51</span><br />
max iterations=<span style="font-family: "Courier New",Courier,monospace;">10,000,000</span><br />
<br />
<b>Render tech</b><br />
Each frame was individually rendered at 1080x1080 resolution (1080p) and
strung together at 30 frames per second. Sidebands were added for compatibility with standard 1920x1080 resolution. No frame interpolation was
used. All images were lovingly rendered by 12 CPU cores running 24/7
for 7 months.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-742237791069860579?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/IFrUGl8YeSoOh7Me8oRyH-EWrUs/0/da"><img src="http://feedads.g.doubleclick.net/~a/IFrUGl8YeSoOh7Me8oRyH-EWrUs/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/IFrUGl8YeSoOh7Me8oRyH-EWrUs/1/da"><img src="http://feedads.g.doubleclick.net/~a/IFrUGl8YeSoOh7Me8oRyH-EWrUs/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/4IFbhTuzIKk" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com2http://fractaljourney.blogspot.com/2011/12/in-memory-of-benoit-mandelbrot.htmltag:blogger.com,1999:blog-62573014049470339.post-19605666135926527382011-04-30T23:28:00.004-04:002011-05-01T23:09:09.771-04:002011-05-01T23:09:09.771-04:00Outtake: Mandelbrot Ultra Zoom #6: 1.0E185<iframe allowfullscreen="" frameborder="0" height="505" src="http://www.youtube.com/embed/USWVZzU3daw?hd=1" width="640"></iframe><br />
<br />
After several abandoned projects (mostly due to render times estimated to be more than 2 years), I finally completed a full zoom.<br />
<br />
<b>Description</b><br />
What is a Mandelbrot zoom blooper? It's what happens when you commit 6 months of computing time on three computers to create something that doesn't turn out the way you expect! The color rotations that begin at 1:36 were unintentional. However, the side effect is that the animation is much more psychedelic than expected due to the color cycling and also brings out details that are not apparent with still images.<br />
<br />
<u>Annotations</u><br />
This animation shows patterns that only a zoom animation reveals - patterns that still images do not convey. For example, note how the "branches" rotate clockwise and counter-clockwise. Furthermore, note how the clockwise rotations double from 2 arms, to 4, to 8, and so on. And note how the counter-clockwise arms also double, although starting from 10. Annotations counting these branches for the first zoom series starts at 0:53.<br />
<br />
And if that's not enough detail, consider that when there are 2 branches, the branches rotate counter-clockwise through a 180 degree sweep before evolving into the clockwise (multiple of ten) pattern. When the counter-clockwise patterns return as 4, the branches rotate through a 90 degree sweep before evolving into the clockwise pattern. The set of 8 branches rotate through a 45 degree sweep, and so forth. This type of periodic doubling is common in this region of the Mandelbrot set, but not necessarily elsewhere in the set.<br />
<br />
<u>Render tech</u><br />
Each frame was individually rendered at 720x480 resolution (480p) and strung together at 30 frames per second. No frame interpolation was used. All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months. A YouTube HD version was created by interpolating images to 1280x720 (720p). Although the visual detail is not better, YouTube appears to afford more than proportionately greater bitrates to 720p content, making the video at 720p appear better than at 480p. <br />
<br />
<b>Music</b><br />
"Martian Invasion" by <a href="http://itunes.apple.com/us/album/suburban-films/id305508932">Dark Flow</a>. (Thanks again!)<br />
<br />
<b>Coordinates</b><br />
Mandelbrot<br />
Final zoom location:<br />
real=<span style="font-family: "Courier New",Courier,monospace;">-0.6367543465</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8238997864</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3739831915</span><br />
<span style="font-family: "Courier New",Courier,monospace;">7140499472</span><br />
<span style="font-family: "Courier New",Courier,monospace;">0360213850</span><br />
<span style="font-family: "Courier New",Courier,monospace;">2943775952</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8815440209</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6249756751</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3223798252</span><br />
<span style="font-family: "Courier New",Courier,monospace;">0103084082</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9591065785</span><br />
<span style="font-family: "Courier New",Courier,monospace;">2387307099</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3324732992</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9252845588</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8339008633</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9317126456</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3425878268</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8785118895</span><br />
<span style="font-family: "Courier New",Courier,monospace;">3461652529</span><br />
<span style="font-family: "Courier New",Courier,monospace;">1202</span><br />
Img=<span style="font-family: "Courier New",Courier,monospace;">0.6850312970</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8367730147</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6087839141</span><br />
<span style="font-family: "Courier New",Courier,monospace;">7437674213</span><br />
<span style="font-family: "Courier New",Courier,monospace;">1010988777</span><br />
<span style="font-family: "Courier New",Courier,monospace;">5075070904</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9508452703</span><br />
<span style="font-family: "Courier New",Courier,monospace;">4567485134</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8147467091</span><br />
<span style="font-family: "Courier New",Courier,monospace;">9233270255</span><br />
<span style="font-family: "Courier New",Courier,monospace;">5722504984</span><br />
<span style="font-family: "Courier New",Courier,monospace;">6615654152</span><br />
<span style="font-family: "Courier New",Courier,monospace;">7052675399</span><br />
<span style="font-family: "Courier New",Courier,monospace;">4100213876</span><br />
<span style="font-family: "Courier New",Courier,monospace;">1943853722</span><br />
<span style="font-family: "Courier New",Courier,monospace;">2657615602</span><br />
<span style="font-family: "Courier New",Courier,monospace;">8819018787</span><br />
<span style="font-family: "Courier New",Courier,monospace;">4239788845</span><br />
<span style="font-family: "Courier New",Courier,monospace;">0551930772</span><br />
<span style="font-family: "Courier New",Courier,monospace;">4466</span><br />
magn=<span style="font-family: "Courier New",Courier,monospace;">1.001113E184</span><br />
max iterations=<span style="font-family: "Courier New",Courier,monospace;">1,000,000</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-1960566613592652738?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/KJ5_eUiAlvoPL8VMyk0yazvLkzM/0/da"><img src="http://feedads.g.doubleclick.net/~a/KJ5_eUiAlvoPL8VMyk0yazvLkzM/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/KJ5_eUiAlvoPL8VMyk0yazvLkzM/1/da"><img src="http://feedads.g.doubleclick.net/~a/KJ5_eUiAlvoPL8VMyk0yazvLkzM/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/gkK3NFGYf40" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com5http://fractaljourney.blogspot.com/2011/04/mandelbrot-ultra-zoom-6-10e185.htmltag:blogger.com,1999:blog-62573014049470339.post-33006350013616737902010-10-16T21:19:00.007-04:002010-10-16T22:31:46.760-04:002010-10-16T22:31:46.760-04:00Benoît Mandelbrot (November 20, 1924 - October 16, 2010)Thanks to <a href="http://gerisullivan.livejournal.com/287287.html">Geri Sullivan</a> and the internet, I can claim to be two degrees of separation from Dr. Mandelbrot. For me, it is an honor just to claim such a superficial relationship to greatness.<br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/_kDnJbLSxPCo/SQKT3W-afxI/AAAAAAAABEA/4ufW74plhXo/s1600/Mandelbrot+at+Ig+Nobel.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="http://4.bp.blogspot.com/_kDnJbLSxPCo/SQKT3W-afxI/AAAAAAAABEA/4ufW74plhXo/s320/Mandelbrot+at+Ig+Nobel.png" width="320" /></a></div><div style="text-align: center;"></div><div style="text-align: center;"><a href="http://fractaljourney.blogspot.com/2008/10/mandelbrot-at-ig-nobel-prizes.html">Dr. Mandelbrot at the 2008 Ig Nobel Awards with Fractal Journey's image</a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/_kDnJbLSxPCo/TLpRcjvY9lI/AAAAAAAACfI/qB1eLKHmmB8/s1600/Untitled.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="179" src="http://2.bp.blogspot.com/_kDnJbLSxPCo/TLpRcjvY9lI/AAAAAAAACfI/qB1eLKHmmB8/s320/Untitled.png" width="320" /></a></div><div style="text-align: center;"> <a href="http://vimeo.com/7911813">Dr. Mandelbrot at the 2009 Ig Nobel Awards (starts at 29:00) with Fractal Journey's image</a><br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/_kDnJbLSxPCo/Rv_Ou4lfQUI/AAAAAAAAAhs/N_6vVAwdVPk/s1600/Mandelbrot_TIA.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/Rv_Ou4lfQUI/AAAAAAAAAhs/N_6vVAwdVPk/s320/Mandelbrot_TIA.png" width="320" /></a></div></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-3300635001361673790?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/iT28cSvKXz440aAjSaC8UKxFS7Y/0/da"><img src="http://feedads.g.doubleclick.net/~a/iT28cSvKXz440aAjSaC8UKxFS7Y/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/iT28cSvKXz440aAjSaC8UKxFS7Y/1/da"><img src="http://feedads.g.doubleclick.net/~a/iT28cSvKXz440aAjSaC8UKxFS7Y/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/FCrd3bRQ9R0" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2010/10/thanks-to-geri-sullivan-and-internet-i.htmltag:blogger.com,1999:blog-62573014049470339.post-65990367894155942412010-03-10T20:47:00.016-05:002011-04-30T23:31:56.099-04:002011-04-30T23:31:56.099-04:00Mandelbrot Assemblage<iframe width="640" height="390" src="http://www.youtube.com/embed/VLtZ5ICXC5g?hd=1" frameborder="0" allowfullscreen></iframe><br />
<br />
<b>Description </b><br />
"Mandelbrot Assemblage" is based on the idea in <a href="http://fractaljourney.blogspot.com/2008/04/mandelbrot-evolution.html">Mandelbrot Birth and Evolution</a> whereby the exponent "n" in the equation z^n+c is manipulated as the principal variable in the animation. However, for this animation, the exponent "n" is decreased from 40 to 2. Furthermore, rather than showing the entire set, the animation zooms in on Seahorse Valley and tracks its evolution as the exponent is reduced to 2. Note that the location is not fixed in this case since the location of Seahorse Valley moves as the exponent is changed.<br />
<br />
<b>Music</b><br />
"Escape" (edited for length) by <a href="http://itunes.apple.com/us/album/suburban-films/id305508932">Dark Flow</a><img alt="" border="0" class=" ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl rtvtwtunkjohuauulmwb rtvtwtunkjohuauulmwb pbnyuuufmpfakcalikbz pbnyuuufmpfakcalikbz gqhcazepwoggmnsfuofc" height="1" src="http://www.assoc-amazon.com/e/ir?t=orswan-20&l=as2&o=1&a=B001U9YCG8" style="border: medium none ! important; margin: 0px ! important;" width="1" />. <br />
<br />
<b>Technical information</b><br />
Each frame was rendered in luxurious 1920x1080 resolution, strung together at 30 frames per second, and encoded at 16Mbps, making this a Full HD animation worthy of your 1080p flatscreen.<br />
<br />
<b>Downloads</b><br />
<a href="http://www.megaupload.com/?d=RGI76798">Download 1080p MP4 (Highest Quality, 1920x1080 - 253MB)</a><br />
<a href="http://www.mediafire.com/?rmt2mt3zmle">Download WMV (Medium Quality, 1280x720 - 116MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-6599036789415594241?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/t8jcY7VeN34FJ4JY1m26VYmy0qI/0/da"><img src="http://feedads.g.doubleclick.net/~a/t8jcY7VeN34FJ4JY1m26VYmy0qI/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/t8jcY7VeN34FJ4JY1m26VYmy0qI/1/da"><img src="http://feedads.g.doubleclick.net/~a/t8jcY7VeN34FJ4JY1m26VYmy0qI/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/e02Wf6yGdQo" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2010/03/mandelbrot-assemblage.htmltag:blogger.com,1999:blog-62573014049470339.post-58069454356434427532010-01-26T22:24:00.007-05:002011-04-30T23:31:11.212-04:002011-04-30T23:31:11.212-04:00Mandelbrot Ultra Zoom #5: 2.1E275<iframe width="640" height="510" src="http://www.youtube.com/embed/0jGaio87u3A" frameborder="0" allowfullscreen></iframe><br />
<br />
<b>Description </b><br />
The final magnification is 2.1x10^275 (or 2^915). I believe that this is the deepest zoom animation of the Mandelbrot set produced to date (January 2010).<br />
<br />
Each frame was individually rendered at 640x480 resolution and strung together at 30 frames per second. No frame interpolation was used. All images were lovingly rendered by 12 CPU cores running 24/7 for 6 months.<br />
<br />
<b>Music</b><br />
"Research Lab" by <a href="http://itunes.apple.com/us/album/suburban-films/id305508932">Dark Flow</a><img alt="" border="0" class=" ygabjfaklrmxmtzqvzyl ygabjfaklrmxmtzqvzyl gqhcazepwoggmnsfuofc" height="1" src="http://www.assoc-amazon.com/e/ir?t=orswan-20&l=as2&o=1&a=B001U9YCG8" style="border: medium none ! important; margin: 0px ! important;" width="1" />.<br />
<br />
<b>Coordinates</b><br />
Mandelbrot<br />
Final zoom location:<br />
real=<span style="font-family: courier new;">-1.7400623825<br />
7933990522<br />
0844167065<br />
8256382966<br />
4172043617<br />
1866879862<br />
4184611829<br />
1964415305<br />
6054840718<br />
3394832257<br />
4345000825<br />
9172138785<br />
4929836778<br />
9336650341<br />
7299549623<br />
7388383033<br />
4646546129<br />
0768441055<br />
4861368707<br />
1985055926<br />
9507357211<br />
7902436669<br />
4013479375<br />
3068611574<br />
7459438207<br />
1288525822<br />
2629105433<br />
6486959460<br />
03865</span><br />
img=<span style="font-family: courier new;">0.0281753397<br />
7921104899<br />
2411521144<br />
3195096875<br />
3907674299<br />
0608570401<br />
3095958801<br />
7432409201<br />
8638540081<br />
4658560553<br />
6156950844<br />
8677407700<br />
0669037710<br />
1916653380<br />
6041899932<br />
4320867147<br />
0287689837<br />
0483131652<br />
7873719459<br />
2645920846<br />
0043315033<br />
3362859318<br />
1020170329<br />
5807479996<br />
6721030307<br />
0821501719<br />
9479847808<br />
9798638258<br />
639934</span><br />
magn=<span style="font-family: courier new;">2.0667172E275</span><br />
max iterations=10,000,000<br />
<br />
<a href="http://www.mediafire.com/?a4iwmzex0wm">Download WMV (640x480 medium quality - 86MB)</a><br />
<a href="http://www.megaupload.com/?d=OD7KCD15">Download MP4 (640x480 medium quality - 234MB)</a><br />
<a href="http://www.megaupload.com/?d=RUXN5LVA">Download WMV (640x480 full quality - 539MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-5806945435643442753?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/pqgdmRIMo-O3TnGBAvewnr4Epew/0/da"><img src="http://feedads.g.doubleclick.net/~a/pqgdmRIMo-O3TnGBAvewnr4Epew/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/pqgdmRIMo-O3TnGBAvewnr4Epew/1/da"><img src="http://feedads.g.doubleclick.net/~a/pqgdmRIMo-O3TnGBAvewnr4Epew/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/hQ_TFN0HiqU" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com5http://fractaljourney.blogspot.com/2010/01/mandelbrot-ultra-zoom-5-21e275.htmltag:blogger.com,1999:blog-62573014049470339.post-87586514042358126392008-11-02T22:35:00.009-05:002010-10-19T21:22:13.850-04:002010-10-19T21:22:13.850-04:00Mandelbrot Ultra Zoom #4: 2.5E194<object height="344" width="425"><param name="movie" value="http://www.youtube.com/v/FkJ2d2krDok&hl=en&fs=1"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"><embed src="http://www.youtube.com/v/FkJ2d2krDok&hl=en&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object><br />
<br />
I believe this is the deepest Mandelbrot zoom video produced to date (November 2008). No pixel interpolation or frame interpolation were used - all images were individually rendered at 640x480 and then strung together at 30 frames per second.<br />
Note that no camera rotation was utilized throughout the animation. This is especially intriguing because the zoom into the targetted filament tip shows the filament rotating around the screen's center. In other words, hidden at the extremity of the filament is a spiral!<br />
<br />
Mandelbrot<br />
Final zoom location:<br />
<span style="font-family: courier new;">real=-1.2963551381<br />
7303621680<br />
8304477845<br />
2822662624<br />
4803862985<br />
5679928775<br />
8134023909<br />
7541015237<br />
4968874495<br />
7013280950<br />
8921264237<br />
1849205069<br />
1873930630<br />
0129984443<br />
1327669662<br />
9091695392<br />
5715912473<br />
5766218195<br />
3641356251<br />
6581747800<br />
63</span><br />
<span style="font-family: courier new;">img=0.4418516057<br />
3519660121<br />
2848580174<br />
9869488384<br />
9923969742<br />
4758901550<br />
7705711715<br />
9588719169<br />
1529341962<br />
7212288799<br />
9691678065<br />
6481371825<br />
1021509265<br />
0641919732<br />
0221562977<br />
4396782935<br />
1836205354<br />
4727941073<br />
7461632018<br />
1517184948<br />
375</span><br />
<span style="font-family: courier new;">magn=2.514908E194</span><br />
<span style="font-family: courier new;">maximum iterations=1,000,000</span><br />
<br />
<a href="http://www.mediafire.com/?w4ziiodxzgm">Download WMV (640x480 medium quality - 86MB)</a><br />
<a href="http://www.mediafire.com/?76d91c8rcgp97jp">Download MP4 (640x480 high quality - 95MB)</a><br />
<a href="http://www.megaupload.com/?d=3K0K22SV">Download WMV (640x480 full quality - 275MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-8758651404235812639?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/O3ZQUoAXmrOUw8-Grew5kSKIuHU/0/da"><img src="http://feedads.g.doubleclick.net/~a/O3ZQUoAXmrOUw8-Grew5kSKIuHU/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/O3ZQUoAXmrOUw8-Grew5kSKIuHU/1/da"><img src="http://feedads.g.doubleclick.net/~a/O3ZQUoAXmrOUw8-Grew5kSKIuHU/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/zhXRcoJ7dq8" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com1http://fractaljourney.blogspot.com/2008/11/mandelbrot-ultra-zoom-4-25e194.htmltag:blogger.com,1999:blog-62573014049470339.post-14762441289215829112008-10-24T23:30:00.008-04:002010-10-16T22:30:43.395-04:002010-10-16T22:30:43.395-04:00Mandelbrot at the 2008 Ig Nobel PrizesMaking an appearance at the 2008 Ig Nobel Awards is Fractal Journey's own Mandelbrot set image, originally posted <a href="http://fractaljourney.blogspot.com/p/introduction.html">here</a>.<br />
<br />
<a href="http://3.bp.blogspot.com/_kDnJbLSxPCo/SQKTrQptE1I/AAAAAAAABD4/1mtUuUzpyRc/s1600-h/Ig+ceremony.png" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5260929686135706450" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/SQKTrQptE1I/AAAAAAAABD4/1mtUuUzpyRc/s400/Ig+ceremony.png" style="cursor: pointer; display: block; height: 224px; margin: 0px auto 10px; text-align: center; width: 400px;" /></a><br />
Who is that standing center stage?<br />
<br />
<a href="http://4.bp.blogspot.com/_kDnJbLSxPCo/SQKT3W-afxI/AAAAAAAABEA/4ufW74plhXo/s1600-h/Mandelbrot+at+Ig+Nobel.png" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5260929893991612178" src="http://4.bp.blogspot.com/_kDnJbLSxPCo/SQKT3W-afxI/AAAAAAAABEA/4ufW74plhXo/s400/Mandelbrot+at+Ig+Nobel.png" style="cursor: pointer; display: block; height: 225px; margin: 0px auto 10px; text-align: center; width: 400px;" /></a>It's Doctor Mandelbrot himself! Thanks to <a href="http://gerisullivan.livejournal.com/">Geri Sullivan</a>. Watch the entire 2008 Ig Nobel Prizes ceremony <a href="http://improbable.com/ig/2008/webcast/stream.html">here</a>.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-1476244128921582911?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/8egO6zR0S2MPhvxUsAomgalcJgU/0/da"><img src="http://feedads.g.doubleclick.net/~a/8egO6zR0S2MPhvxUsAomgalcJgU/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/8egO6zR0S2MPhvxUsAomgalcJgU/1/da"><img src="http://feedads.g.doubleclick.net/~a/8egO6zR0S2MPhvxUsAomgalcJgU/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/0hNl-QYGO6Y" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com1http://fractaljourney.blogspot.com/2008/10/mandelbrot-at-ig-nobel-prizes.htmltag:blogger.com,1999:blog-62573014049470339.post-63121839818090574462008-08-29T23:25:00.004-04:002009-10-19T00:06:50.479-04:002009-10-19T00:06:50.479-04:00Mandelbrot Ultra Zoom #3: 1.1E101<object height="344" width="425"><param name="movie" value="http://www.youtube.com/v/jwk6EENcs4o&hl=en&fs=1"><param name="allowFullScreen" value="true"><embed src="http://www.youtube.com/v/jwk6EENcs4o&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" height="344" width="425"></embed></object><br /><br />Mandelbrot<br />Final zoom location:<br /><span style="font-family:courier new;">real=-1.5752046532<br />8054518627<br />7209903318<br />4298627716<br />1997610841<br />0897527488<br />6072417169<br />2842426068<br />8170553920<br />8484631327<br />9584803247<br />5</span><br /><span style="font-family:courier new;">img=0.0173616212<br />6272928184<br />8431301085<br />0175044293<br />8051875985<br />9190469582<br />1406242723<br />7361755591<br />1001831187<br />2512274494<br />6906225339<br />42</span><br /><span style="font-family:courier new;">magn=1.3293492E101</span><br /><br /><a href="http://www.mediafire.com/?ummtzrgii0n">Download WMV (640x480 full quality - 60MB)</a><br /><a href="http://www.mediafire.com/?4ijnymcfnvg">Download WMV (640x480 medium quality - 12MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-6312183981809057446?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/aKVKN0Hx7lll0lvhPkaUJYLvnlY/0/da"><img src="http://feedads.g.doubleclick.net/~a/aKVKN0Hx7lll0lvhPkaUJYLvnlY/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/aKVKN0Hx7lll0lvhPkaUJYLvnlY/1/da"><img src="http://feedads.g.doubleclick.net/~a/aKVKN0Hx7lll0lvhPkaUJYLvnlY/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/fEJ3b0E1Zas" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/08/mandelbrot-ultra-zoom-3-11e101.htmltag:blogger.com,1999:blog-62573014049470339.post-49305572323371333742008-08-28T23:03:00.003-04:002008-08-28T23:06:34.242-04:002008-08-28T23:06:34.242-04:00Thunder Front<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_kDnJbLSxPCo/SLdnRAZhSBI/AAAAAAAAA_A/8w5mY-f6PQk/s1600-h/jut2a.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/SLdnRAZhSBI/AAAAAAAAA_A/8w5mY-f6PQk/s200/jut2a.png" alt="" id="BLOGGER_PHOTO_ID_5239770233331337234" border="0" /></a><br /><span style="font-family:courier new;">Mandelbrot</span><br /><span style="font-family:courier new;">real=-1.2963551381<br />7303621680<br />8304477845<br />2822662624<br />4803862985<br />56799287</span><span style="font-family:courier new;">75<br />8134023909<br />7541015237<br />4968874495<br />7026302523<br />455</span><br /><span style="font-family:courier new;">img=0.4418516057<br />3519660121</span><span style="font-family:courier new;"><br />2848580174<br />9869488384<br />9923969742<br />4758901550<br />7705711715<br />9588719169<br />15293419</span><span style="font-family:courier new;">62<br />7209673773<br />122</span><br /><span style="font-family:courier new;">magn=8.7793873E92</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-4930557232337133374?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/T2tjcXadIB2jZ7Rk61b-UApyvkM/0/da"><img src="http://feedads.g.doubleclick.net/~a/T2tjcXadIB2jZ7Rk61b-UApyvkM/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/T2tjcXadIB2jZ7Rk61b-UApyvkM/1/da"><img src="http://feedads.g.doubleclick.net/~a/T2tjcXadIB2jZ7Rk61b-UApyvkM/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/ZzWROsPPZxc" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/08/wave-front.htmltag:blogger.com,1999:blog-62573014049470339.post-29750654603928961832008-08-17T22:44:00.003-04:002008-08-18T08:48:17.239-04:002008-08-18T08:48:17.239-04:00Stand-off<a href="http://3.bp.blogspot.com/_kDnJbLSxPCo/SKlvgPTXmWI/AAAAAAAAA4s/fys8vfqADKs/s1600-h/Elephant1_1_c.png"><img id="BLOGGER_PHOTO_ID_5235838641449179490" style="DISPLAY: block; MARGIN: 0px auto 10px; CURSOR: hand; TEXT-ALIGN: center" alt="" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/SKlvgPTXmWI/AAAAAAAAA4s/fys8vfqADKs/s200/Elephant1_1_c.png" border="0" /></a> <div></div><br /><div>Mandelbrot<br />real=0.2500000011222610427628<br />img=0<br />magn=1.3800134E13</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-2975065460392896183?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/0uVBi3FbHTGny4qC1s_XmZrkdBc/0/da"><img src="http://feedads.g.doubleclick.net/~a/0uVBi3FbHTGny4qC1s_XmZrkdBc/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/0uVBi3FbHTGny4qC1s_XmZrkdBc/1/da"><img src="http://feedads.g.doubleclick.net/~a/0uVBi3FbHTGny4qC1s_XmZrkdBc/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/rQ5Z43z_F_E" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/08/stand-off.htmltag:blogger.com,1999:blog-62573014049470339.post-2132468418452789942008-08-01T23:04:00.005-04:002008-08-01T23:45:34.039-04:002008-08-01T23:45:34.039-04:00Mandelbrot Ultra Zoom #2: 3.1E62<object height="344" width="425"><param name="movie" value="http://www.youtube.com/v/9UBjAXqhN2o&hl=en&fs=1"><param name="allowFullScreen" value="true"><embed src="http://www.youtube.com/v/9UBjAXqhN2o&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" height="344" width="425"></embed></object><br /><br /><span style="font-family:courier new;"><br /><span style="font-family:arial;">The final zoom location is:</span><br />Mandelbrot</span><br /><span style="font-family:courier new;">real=-1.9272090522</span><br /><span style="font-family:courier new;">0160524854</span><br /><span style="font-family:courier new;">8683022726</span><br /><span style="font-family:courier new;">6648919007</span><br /><span style="font-family:courier new;">8978777279</span><br /><span style="font-family:courier new;">5578090286</span><br /><span style="font-family:courier new;">8398122533</span><br /><span style="font-family:courier new;">5</span><br /><span style="font-family:courier new;">img=5.7603733586</span><br /><span style="font-family:courier new;">1494214094</span><br /><span style="font-family:courier new;">3702029698</span><br /><span style="font-family:courier new;">1997525561</span><br /><span style="font-family:courier new;">6580550586</span><br /><span style="font-family:courier new;">9379592335</span><br /><span style="font-family:courier new;">2630065555</span><br /><span style="font-family:courier new;">55e-6</span><br /><span style="font-family:courier new;">magn=3.1402835E62<br /><br /><a href="http://www.mediafire.com/?tcyyjybctp4"><span style="font-family:arial;">Download WMV (640x480 medium quality - 52MB)</span></a><br /></span><a href="http://www.megaupload.com/?d=DTH9ALI6"><span style="font-family: arial;">Download WMV (640x480 full quality - 144MB)</span></a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-213246841845278994?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/NuvyhE5vPvKblG0RTK0aZAAvkQs/0/da"><img src="http://feedads.g.doubleclick.net/~a/NuvyhE5vPvKblG0RTK0aZAAvkQs/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/NuvyhE5vPvKblG0RTK0aZAAvkQs/1/da"><img src="http://feedads.g.doubleclick.net/~a/NuvyhE5vPvKblG0RTK0aZAAvkQs/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/bXxMLseDOQc" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/08/mandelbrot-ultra-zoom-2.htmltag:blogger.com,1999:blog-62573014049470339.post-22971916448792867022008-07-20T18:52:00.014-04:002008-08-01T23:43:31.867-04:002008-08-01T23:43:31.867-04:00Mandelbrot Ultra Zoom #1: 1.4E114I believe this is the deepest Mandelbrot zoom animation ever created. Enjoy!<br /><br /><object height="344" width="425"><param name="movie" value="http://www.youtube.com/v/J5ffjRI5VlU&hl=en&fs=1"><param name="allowFullScreen" value="true"><embed src="http://www.youtube.com/v/J5ffjRI5VlU&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" height="344" width="425"></embed></object><br /><br />The final zoom location is:<br /><span style="font-family:courier new;">Real= -0.0067765229<br />5833245729<br />6422637819<br />8462725635<br />6509565412<br />9704315829<br />3730243670<br />9978497196<br />4011657746<br />9208811170<br />9565911618<br />0305835245<br />625103<br /><br /></span><span style="font-family:courier new;">Img= 1.0035834658<br />8202262420<br />1979689656<br />4898861775<br />5127635794<br />1488567579<br />5600746635<br />7858474318<br />0718284163<br />1101081545<br />8067773390<br />2938764201<br />6275<br /><br /></span><span style="font-family:courier new;">Magn=1.3775006E114</span><br /><br /><a href="http://www.mediafire.com/?br1d9j3mtvj">Download WMV (640x480 medium quality - 98MB)</a><br /><a href="http://www.megaupload.com/?d=ADZ2VILY">Download WMV (640x480 full quality - 227MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-2297191644879286702?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/Z4sM4q5eRnUSIhDcKUjgMsXgSco/0/da"><img src="http://feedads.g.doubleclick.net/~a/Z4sM4q5eRnUSIhDcKUjgMsXgSco/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/Z4sM4q5eRnUSIhDcKUjgMsXgSco/1/da"><img src="http://feedads.g.doubleclick.net/~a/Z4sM4q5eRnUSIhDcKUjgMsXgSco/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/4MtU4Kn_eLw" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/07/mandelbrot-ultra-zoom-1.htmltag:blogger.com,1999:blog-62573014049470339.post-46865289608203481442008-05-23T15:25:00.005-04:002008-08-15T23:32:49.436-04:002008-08-15T23:32:49.436-04:00Seahorse Valley Tour (version 2)<div style="text-align: center;"><br /></div><object height="355" width="425"><param name="movie" value="http://www.youtube.com/v/kwyBdKbb_18&hl=en"><param name="wmode" value="transparent"><embed src="http://www.youtube.com/v/kwyBdKbb_18&hl=en" type="application/x-shockwave-flash" wmode="transparent" height="355" width="425"></embed></object><br /><br /><a href="http://www.mediafire.com/?1rlob2odg6b">Download WMV (640x480 medium quality - 72MB)</a><br /><a href="http://www.megaupload.com/?d=5YFA3W8Y">Download WMV (640x480 full quality - 184MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-4686528960820348144?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/Y5FYazdeGDn2Svdxhz4fbia6TKg/0/da"><img src="http://feedads.g.doubleclick.net/~a/Y5FYazdeGDn2Svdxhz4fbia6TKg/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/Y5FYazdeGDn2Svdxhz4fbia6TKg/1/da"><img src="http://feedads.g.doubleclick.net/~a/Y5FYazdeGDn2Svdxhz4fbia6TKg/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/q3V7y6GCQxw" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/05/seahorse-valley-tour-version-2.htmltag:blogger.com,1999:blog-62573014049470339.post-73604048757429600312008-05-12T12:14:00.004-04:002008-12-09T18:28:18.051-05:002008-12-09T18:28:18.051-05:00Acid Galaxy<a href="http://3.bp.blogspot.com/_kDnJbLSxPCo/SChuNrv-ORI/AAAAAAAAA0Q/z-oYGRVf8lc/s1600-h/deep4.png"><img id="BLOGGER_PHOTO_ID_5199526951160527122" style="margin: 0px auto 10px; display: block; text-align: center;" alt="" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/SChuNrv-ORI/AAAAAAAAA0Q/z-oYGRVf8lc/s200/deep4.png" border="0" /></a><span style="font-family: courier new;">Mandelbrot</span><br /><div style="font-family: courier new;">real=-0.0067765229<br />5833245729<br />6422637819<br />8462725635<br />4012783794<br />0175251667<br />3439809031<br />5205544783<br />2474372647<br />9432245112<br />1031244649<br />7782690998<br />06940775<br /><br /></div><div style="font-family: courier new;">img=1.0035834658<br />8202262420<br />1979689656<br />4898861775<br />3713225333<br />8685572979<br />2045977175<br />1943762419<br />3108457293<br />8334399372<br />2968031058<br />5246299325<br />209<br /><br />magn=6.068204E115</div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-7360404875742960031?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/E7KMgNfwzMlAFLH8e-WNVuzf640/0/da"><img src="http://feedads.g.doubleclick.net/~a/E7KMgNfwzMlAFLH8e-WNVuzf640/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/E7KMgNfwzMlAFLH8e-WNVuzf640/1/da"><img src="http://feedads.g.doubleclick.net/~a/E7KMgNfwzMlAFLH8e-WNVuzf640/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/n21z5OrNuf0" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/05/acid-galaxy.htmltag:blogger.com,1999:blog-62573014049470339.post-39949311311169905842008-04-27T16:18:00.004-04:002008-08-15T23:13:08.730-04:002008-08-15T23:13:08.730-04:00Mandelbrot Evolution<div style="text-align: center;"><br /><a style="left: 348px ! important; top: 15px ! important;" title="Click here to block this object with Adblock Plus" class="abp-objtab-0508680677823436 visible" href="http://www.youtube.com/v/kcr6eLXrmW8"></a><object height="350" width="425"> <param name="movie" value="http://www.youtube.com/v/kcr6eLXrmW8"> <embed src="http://www.youtube.com/v/kcr6eLXrmW8" type="application/x-shockwave-flash" height="350" width="425"></embed> </object><br /></div><br /><br /><a href="http://www.mediafire.com/?3ekimpetutc">Download WMV (640x480 - 23MB)</a><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-3994931131116990584?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/z_nxaNsd9jr9akizZQqjmCFxlA4/0/da"><img src="http://feedads.g.doubleclick.net/~a/z_nxaNsd9jr9akizZQqjmCFxlA4/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/z_nxaNsd9jr9akizZQqjmCFxlA4/1/da"><img src="http://feedads.g.doubleclick.net/~a/z_nxaNsd9jr9akizZQqjmCFxlA4/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/b-Iq8p2sNBI" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/04/mandelbrot-evolution.htmltag:blogger.com,1999:blog-62573014049470339.post-25705425579938485962008-04-23T14:25:00.003-04:002008-12-09T18:28:18.216-05:002008-12-09T18:28:18.216-05:00Astronaut<a href="http://3.bp.blogspot.com/_kDnJbLSxPCo/SA9_I_m2TaI/AAAAAAAAA0I/DvbZsiXDx3M/s1600-h/Elephant1.png"><img id="BLOGGER_PHOTO_ID_5192508687871528354" style="margin: 0px auto 10px; display: block; text-align: center;" alt="" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/SA9_I_m2TaI/AAAAAAAAA0I/DvbZsiXDx3M/s200/Elephant1.png" border="0" /></a><br /><div><span style="font-family: courier new;">Mandelbrot</span><br /><span style="font-family: courier new;">Real=-1.623630873494682184</span><br /><span style="font-family: courier new;">Img=1.687884317950000000000009e-8</span><br /><span style="font-family: courier new;">Magn=2.2429907E15</span><br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-2570542557993848596?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/u_1vCBWaOQLO9rlEgCTUWJo7mUQ/0/da"><img src="http://feedads.g.doubleclick.net/~a/u_1vCBWaOQLO9rlEgCTUWJo7mUQ/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/u_1vCBWaOQLO9rlEgCTUWJo7mUQ/1/da"><img src="http://feedads.g.doubleclick.net/~a/u_1vCBWaOQLO9rlEgCTUWJo7mUQ/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/QXbxf55zHtw" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/04/astronaut.htmltag:blogger.com,1999:blog-62573014049470339.post-41883312089646822192008-04-23T14:24:00.003-04:002008-12-09T18:28:18.451-05:002008-12-09T18:28:18.451-05:00Duck<a href="http://1.bp.blogspot.com/_kDnJbLSxPCo/SA9-9fm2TZI/AAAAAAAAA0A/dXqmZbHZfPA/s1600-h/Elephant2.png"><img id="BLOGGER_PHOTO_ID_5192508490303032722" style="margin: 0px auto 10px; display: block; text-align: center;" alt="" src="http://1.bp.blogspot.com/_kDnJbLSxPCo/SA9-9fm2TZI/AAAAAAAAA0A/dXqmZbHZfPA/s200/Elephant2.png" border="0" /></a><br /><div><span style="font-family: courier new;">Mandelbrot</span><br /><span style="font-family: courier new;">Real=-1.6236308734946817743906335</span><br /><span style="font-family: courier new;">Img=1.6878843238015623805306065e-8</span><br /><span style="font-family: courier new;">Magn=2.8332514E16</span><br /></div><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-4188331208964682219?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/-1FIgLow_cE3Tph7Z2gRiHtfelk/0/da"><img src="http://feedads.g.doubleclick.net/~a/-1FIgLow_cE3Tph7Z2gRiHtfelk/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/-1FIgLow_cE3Tph7Z2gRiHtfelk/1/da"><img src="http://feedads.g.doubleclick.net/~a/-1FIgLow_cE3Tph7Z2gRiHtfelk/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/OwGYUQ8ek98" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/04/mandelbrot.htmltag:blogger.com,1999:blog-62573014049470339.post-20188416876469593992008-02-18T23:38:00.003-05:002008-12-09T18:28:18.810-05:002008-12-09T18:28:18.810-05:00Flame Through<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_kDnJbLSxPCo/R7pddFzS8DI/AAAAAAAAAyA/Au9U2j64hL4/s1600-h/waves2.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/R7pddFzS8DI/AAAAAAAAAyA/Au9U2j64hL4/s200/waves2.png" alt="" id="BLOGGER_PHOTO_ID_5168546276715982898" border="0" /></a><br />Mandelbrot (Orbit Traps)<br />real=-1.23174033469712322286<br />img=0.318857054527170675267<br />magn=2.0917186E11 angle=62.3082<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-2018841687646959399?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/ymp_EXrCcGjXfEvG0317SXOvID0/0/da"><img src="http://feedads.g.doubleclick.net/~a/ymp_EXrCcGjXfEvG0317SXOvID0/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/ymp_EXrCcGjXfEvG0317SXOvID0/1/da"><img src="http://feedads.g.doubleclick.net/~a/ymp_EXrCcGjXfEvG0317SXOvID0/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/i0VLywlRrU4" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2008/02/mandelbrot-orbit-traps-real-1.htmltag:blogger.com,1999:blog-62573014049470339.post-73121913421093264402007-12-15T23:43:00.001-05:002008-12-09T18:28:18.917-05:002008-12-09T18:28:18.917-05:00Flare<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_kDnJbLSxPCo/R2StT565-5I/AAAAAAAAAk0/_tcOWe6zQV0/s1600-h/waves1.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://3.bp.blogspot.com/_kDnJbLSxPCo/R2StT565-5I/AAAAAAAAAk0/_tcOWe6zQV0/s200/waves1.png" alt="" id="BLOGGER_PHOTO_ID_5144427231840959378" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-1.23174037498509755</span><br /><span style="font-family: courier new;">img=0.31885704886547276</span><br /><span style="font-family: courier new;">magn=95870437</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-7312191342109326440?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/dcjHZBmLDpFdYk-E3D3KeIz1ko8/0/da"><img src="http://feedads.g.doubleclick.net/~a/dcjHZBmLDpFdYk-E3D3KeIz1ko8/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/dcjHZBmLDpFdYk-E3D3KeIz1ko8/1/da"><img src="http://feedads.g.doubleclick.net/~a/dcjHZBmLDpFdYk-E3D3KeIz1ko8/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/YkbAMj_KIkY" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/12/splash.htmltag:blogger.com,1999:blog-62573014049470339.post-5093071091858290462007-10-17T00:16:00.002-04:002008-12-09T18:28:19.100-05:002008-12-09T18:28:19.100-05:00Bromeliad<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_kDnJbLSxPCo/RxWM64lfQaI/AAAAAAAAAiU/buGvudQK7Cw/s1600-h/breeze2.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://2.bp.blogspot.com/_kDnJbLSxPCo/RxWM64lfQaI/AAAAAAAAAiU/buGvudQK7Cw/s200/breeze2.png" alt="" id="BLOGGER_PHOTO_ID_5122155094453731746" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-0.1410208714056796086</span><br /><span style="font-family: courier new;">img=0.64931169246820762125</span><br /><span style="font-family: courier new;">magn=8.602555E9</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-509307109185829046?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/mQfzA-W6WJYEzeeaLTWf_QDka1g/0/da"><img src="http://feedads.g.doubleclick.net/~a/mQfzA-W6WJYEzeeaLTWf_QDka1g/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/mQfzA-W6WJYEzeeaLTWf_QDka1g/1/da"><img src="http://feedads.g.doubleclick.net/~a/mQfzA-W6WJYEzeeaLTWf_QDka1g/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/NUiYLcfSOP4" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/10/bromeliad.htmltag:blogger.com,1999:blog-62573014049470339.post-89101384739188564902007-10-16T23:18:00.002-04:002008-12-09T18:28:19.528-05:002008-12-09T18:28:19.528-05:00Reach<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_kDnJbLSxPCo/RxV_RYlfQYI/AAAAAAAAAiI/eAbQZ5IOZtI/s1600-h/breeze1.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://4.bp.blogspot.com/_kDnJbLSxPCo/RxV_RYlfQYI/AAAAAAAAAiI/eAbQZ5IOZtI/s200/breeze1.png" alt="" id="BLOGGER_PHOTO_ID_5122140087837999490" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-0.1410231956630216</span><br /><span style="font-family: courier new;">img=0.64931493696439025</span><br /><span style="font-family: courier new;">magn=1310545.5</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-8910138473918856490?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/QaOOUueDWS001015E6xLSulRSRg/0/da"><img src="http://feedads.g.doubleclick.net/~a/QaOOUueDWS001015E6xLSulRSRg/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/QaOOUueDWS001015E6xLSulRSRg/1/da"><img src="http://feedads.g.doubleclick.net/~a/QaOOUueDWS001015E6xLSulRSRg/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/8zX8kQwp10I" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/10/reach.htmltag:blogger.com,1999:blog-62573014049470339.post-75562621409339776952007-10-07T14:15:00.001-04:002008-12-09T18:28:19.677-05:002008-12-09T18:28:19.677-05:00Alien Shell<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_kDnJbLSxPCo/RwkimYlfQWI/AAAAAAAAAh8/qCBHtyiweFo/s1600-h/dandel2a_ot.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://4.bp.blogspot.com/_kDnJbLSxPCo/RwkimYlfQWI/AAAAAAAAAh8/qCBHtyiweFo/s200/dandel2a_ot.png" alt="" id="BLOGGER_PHOTO_ID_5118660494313341282" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit trap)</span><br /><span style="font-family: courier new;">real=-1.416569537007931794767370213294212355</span><br /><span style="font-family: courier new;">img=4.93271189808742837552590413869772732e-14</span><br /><span style="font-family: courier new;">magn=2.8696644E26</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-7556262140933977695?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/joF2Y3RjOBkEz_Slrh4GMnsXRCc/0/da"><img src="http://feedads.g.doubleclick.net/~a/joF2Y3RjOBkEz_Slrh4GMnsXRCc/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/joF2Y3RjOBkEz_Slrh4GMnsXRCc/1/da"><img src="http://feedads.g.doubleclick.net/~a/joF2Y3RjOBkEz_Slrh4GMnsXRCc/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/2ISRbE4uGPM" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/10/biohazard-shell.htmltag:blogger.com,1999:blog-62573014049470339.post-18422340615017117172007-10-01T23:21:00.002-04:002008-12-09T18:28:20.365-05:002008-12-09T18:28:20.365-05:00Rose Dream<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_kDnJbLSxPCo/RwG5a4lfQVI/AAAAAAAAAh0/2EwPIFPpMjY/s1600-h/whizzer_ot.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://2.bp.blogspot.com/_kDnJbLSxPCo/RwG5a4lfQVI/AAAAAAAAAh0/2EwPIFPpMjY/s200/whizzer_ot.png" alt="" id="BLOGGER_PHOTO_ID_5116574523186954578" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-0.98031384369051721875548</span><br /><span style="font-family: courier new;">img=0.251429708976454016806405</span><br /><span style="font-family: courier new;">magn=8.6894401E12</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-1842234061501711717?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/w2Vy4N2Y1s0M2cFXBx9AykFO2Q8/0/da"><img src="http://feedads.g.doubleclick.net/~a/w2Vy4N2Y1s0M2cFXBx9AykFO2Q8/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/w2Vy4N2Y1s0M2cFXBx9AykFO2Q8/1/da"><img src="http://feedads.g.doubleclick.net/~a/w2Vy4N2Y1s0M2cFXBx9AykFO2Q8/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/u2CiQ1PgGYM" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/10/rose-dream.htmltag:blogger.com,1999:blog-62573014049470339.post-70909361874210777832007-09-24T05:32:00.001-04:002008-12-09T18:28:20.532-05:002008-12-09T18:28:20.532-05:00Ignite<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_kDnJbLSxPCo/RveElYlfQSI/AAAAAAAAAgg/sDD70sG5WK8/s1600-h/tip1.png"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="http://2.bp.blogspot.com/_kDnJbLSxPCo/RveElYlfQSI/AAAAAAAAAgg/sDD70sG5WK8/s200/tip1.png" alt="" id="BLOGGER_PHOTO_ID_5113701679692202274" border="0" /></a><span style="font-family: courier new;">Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-1.40217715024957224118860189522</span><br /><span style="font-family: courier new;">img0.0296448148457388461995792506491</span><br /><span style="font-family: courier new;">magn=6.529072E20</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-7090936187421077783?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/khUjX8O_EqaN8taQbWDawhCX59I/0/da"><img src="http://feedads.g.doubleclick.net/~a/khUjX8O_EqaN8taQbWDawhCX59I/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/khUjX8O_EqaN8taQbWDawhCX59I/1/da"><img src="http://feedads.g.doubleclick.net/~a/khUjX8O_EqaN8taQbWDawhCX59I/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/nu043dG2IJI" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/09/ignite.htmltag:blogger.com,1999:blog-62573014049470339.post-47655320236145900422007-09-20T00:07:00.002-04:002008-12-09T18:28:20.647-05:002008-12-09T18:28:20.647-05:00Laserbrot<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_kDnJbLSxPCo/RvHyWLtYmzI/AAAAAAAAAgY/J0q_D17egdw/s1600-h/magic1.png"><img id="BLOGGER_PHOTO_ID_5112133514956413746" style="margin: 0px auto 10px; display: block; cursor: pointer; text-align: center;" alt="" src="http://4.bp.blogspot.com/_kDnJbLSxPCo/RvHyWLtYmzI/AAAAAAAAAgY/J0q_D17egdw/s200/magic1.png" border="0" /></a><span style="font-family: courier new;"> Mandelbrot (orbit traps)</span><br /><span style="font-family: courier new;">real=-1.38973902765952378011715</span><br /><span style="font-family: courier new;">img=0.10560288702640211145785</span><br /><span style="font-family: courier new;">magn=5.0459934E12</span><div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/62573014049470339-4765532023614590042?l=fractaljourney.blogspot.com' alt='' /></div>
<p><a href="http://feedads.g.doubleclick.net/~a/wXqlx5XuYf7L0te1qBcBpcj9HLk/0/da"><img src="http://feedads.g.doubleclick.net/~a/wXqlx5XuYf7L0te1qBcBpcj9HLk/0/di" border="0" ismap="true"></img></a><br/>
<a href="http://feedads.g.doubleclick.net/~a/wXqlx5XuYf7L0te1qBcBpcj9HLk/1/da"><img src="http://feedads.g.doubleclick.net/~a/wXqlx5XuYf7L0te1qBcBpcj9HLk/1/di" border="0" ismap="true"></img></a></p><img src="http://feeds.feedburner.com/~r/FractalJourney/~4/Y2LHswFogRQ" height="1" width="1"/>Orson Wanghttp://www.blogger.com/profile/03336013668591821868noreply@blogger.com0http://fractaljourney.blogspot.com/2007/09/laserbrot.html