tag:blogger.com,1999:blog-53018217581216262232017-01-15T05:51:10.619-08:00Mathematical paintings and sculpturesHere you can see artworks and sculptures in which mathematical laws were posed as basis. Artworks by M.C. Escher and his followers.Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.comBlogger81125tag:blogger.com,1999:blog-5301821758121626223.post-88140873687284026382014-08-17T11:50:00.000-07:002014-08-17T11:50:32.874-07:00The Art of Deception
Yesterday, I received a copy of book "The Art of Deception" by Brad Honeycutt. This is an excellent compilation of different kind of optical illusions, which were artistically represented by many modern artists around the world.
There were presented on only traditional techniques of art, but also marquetry, sculpture and others.
This book should be in collection of everyone, who interested <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/KBjhBL7uSxA" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com0http://mathpaint.blogspot.com/2014/08/the-art-of-deception.htmltag:blogger.com,1999:blog-5301821758121626223.post-63179980857167343652014-04-24T11:27:00.002-07:002014-04-24T11:27:39.164-07:00Illusion - Confusion
Recently, I received a book "Illusion - Confusion" by Paul Baars, in which he collected examples of almost all known kinds of illusions. There's a lagre section about impossible figures in the book. Among other images, there's one my impossible figure published there.
The distinctive feature of the book is using double page spread for representing large images. For example, <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/SewqA8lyGOE" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2014/04/illusion-confusion.htmltag:blogger.com,1999:blog-5301821758121626223.post-89978861872826404642013-09-21T11:21:00.000-07:002013-09-21T11:21:21.550-07:00Wooden work by Michael Cheshire
Today I received a wooden work by Michael Cheshire. It's one of his series of artworks with cats. Here, you can see a cat looking at huge moon. The scene is decorated by impossible frame.
Michael Cheshire creates his works from many kinds of wood. You can see more his works and by them at his web site http://www.woodenart.com.au/
<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/3iVlUQjvx50" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2013/09/wooden-work-by-michael-cheshire.htmltag:blogger.com,1999:blog-5301821758121626223.post-75220063109134990822013-06-23T11:50:00.000-07:002013-06-23T11:50:02.160-07:00Spiral trees
Trees are the great form of nature and this the shape made many inspiration for numerous artists of mathematical art. I've posted several collections of fractal trees and pythagoras trees. And we've also met with combination of tree-like shape with spiral. Spirals are one of basic mathematical shapes and they are harmoniously match to branchy tree figure. Also spiral is the shape that very <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/OSmfGwBQNrk" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2013/06/spiral-trees.htmltag:blogger.com,1999:blog-5301821758121626223.post-3829531442694499802012-08-07T11:17:00.000-07:002012-08-07T12:22:03.193-07:00The Art of the Illusion
Today I have received a copy of a book by Brad Honeycutt and Terry Stickels "The Art of the Illusion", which consists of more than 200 wonderful images of optical illusions, which were created by many artists all around the world. Artworks by such famous artists as M.C. Escher, Jos de Mey, Rob Gonsalved are combined with artworks by many modern artists, who devoted their lives to creation <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/QWqgOsfELX0" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2012/08/the-art-of-illusion.htmltag:blogger.com,1999:blog-5301821758121626223.post-91980823363953970222011-05-15T12:54:00.000-07:002011-05-15T12:54:04.727-07:00Fractal fonts
The letter A above consists of many Sierpinski triangles, blank spaces of which are colored black. Using of triangular grid to form letter gives some Gothic effect. Font designer Frodo7 created a font Sierpinski Black using such principle, which consist of 87 characters inluding Latin capital and lower letters and numbers. A sample pattern of the font is represented below. Artist created several<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/ATMnyGIBb08" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2011/05/fractal-fonts.htmltag:blogger.com,1999:blog-5301821758121626223.post-59318151081483124382010-11-16T11:04:00.000-08:002010-11-16T11:19:39.254-08:00Calendar 2011A new block calendar on year 2011 was designed at Paul Baars Design. As the calendar 2010 this one contains of 365 various optical illusions. With it you will begin every new day of 2010 year from new unique illusory image of such famous artists as M.C. Escher, Jos de Mey and Istvan Orosz or less known but not less interesting artists.It's very valuable for me that one of my impossible figures <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/22nE9ZjOTjo" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com4http://mathpaint.blogspot.com/2010/11/calendar-2011.htmltag:blogger.com,1999:blog-5301821758121626223.post-43197955543310411522010-09-06T10:49:00.001-07:002010-09-07T08:35:15.220-07:00New set of fractal trees - 2Today, I represent a small but nevertheless interesting set of fractal trees of various kinds.Two mystical fractal trees by Jacob Ankney (Jeddaka).A new variation of Pythagoras tree with curl as base figure for duplication in fractal, which was created by IDeviant.And, in conclusion two fractal images from Shutterstock. The first can be bought here, the second is no longer represented there.<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/fpsovqZsUwk" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2010/09/new-set-of-fractal-trees-2.htmltag:blogger.com,1999:blog-5301821758121626223.post-31552418254997792752010-06-26T12:08:00.000-07:002010-06-27T04:05:14.828-07:00Jos de Mey: Illusionistische MalereiA great book Jos de Mey: Illusionistische Malerei was issued by Edition Virgines in Düsseldorf in 2010. The book describes the life and work of Belgian artist Jos de Mey who devoted his life to drawing impossible figures. Jos de Mey (1928-2007) studied at the Royal Academy of Fine Art in Ghent (Belgium). Then he spent 39 year to teaching interrior design and color there. Since 1968 he had <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/NuY3YbbxFDw" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2010/06/jos-de-mey-illusionistische-malerei.htmltag:blogger.com,1999:blog-5301821758121626223.post-28209909256636693032009-12-12T08:19:00.000-08:002009-12-12T10:23:13.590-08:00Fractal architectureNot only abstract images can be created with fractals, but also very impressive images of strange towers and temples. Some time before I posted fractal image of a fractal temple. Now, the next some surrealistic images of fractal towers are represented below.Medieval fractal (by Ramiro Perez)Sunset Castle (by Ramiro Perez)Ivory Tower - 2 (by Stefan Vitanov)Airy (by Stefan Vitanov)More images of <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/x5RM-WpTPKk" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com4http://mathpaint.blogspot.com/2009/12/fractal-architecture.htmltag:blogger.com,1999:blog-5301821758121626223.post-52182868900233349392009-12-06T10:45:00.001-08:002009-12-06T11:25:38.250-08:00MandelbulbThe Mandelbrot set is one of the most known fractal. It can be seen on many sites and images over the Internet. It was represented in many variations. Today, many fractal artists create beautiful images, which are based on it. But all this time it remained only a two dimensional fractal.Of course, many artists created 3D images with it. Below you can see the Mandelbrot fractal (to the left) and <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/JOzx_wuaEVw" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2009/12/mandelbulb.htmltag:blogger.com,1999:blog-5301821758121626223.post-22426762506827719852009-11-22T11:02:00.000-08:002009-11-22T11:54:17.306-08:00Artforms of Nature and fractalsThe nineteen century German biologist Ernst Haeckel is famous for his fantastically illustrated book Artforms of Nature. The copyright for this book from 1904 has now expired and thanks to Wikimedia Commons it is available for everyone to appreciate.Haekel's artistic interpretation of the biological forms he studied have a clarity of symmetry and detail that has been a source of inspiration for <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/-LSnyrG5c_M" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2009/11/artforms-of-nature-and-fractals.htmltag:blogger.com,1999:blog-5301821758121626223.post-85799912864195365662009-10-06T10:10:00.000-07:002009-10-06T11:48:16.599-07:00Mini books of Anatoly KonenkoYesterday, I received the smallest book of those that I have ever hold in my hands, which is entitled as "Secrets of impossible figures". The dimensions of the book are 3x5 cm. You can compare it's size with a 1 euro coin on the photo above. The book is filled of images of impossible figures. It was published in very limited edition, only 30 copies.The author of the book is Anatoly Konenko from <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/DwR8pH7T-u4" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2009/10/mini-books-of-anatoly-konenko.htmltag:blogger.com,1999:blog-5301821758121626223.post-33016530263218682122009-07-12T05:32:00.000-07:002009-07-12T06:12:36.007-07:00The Great Wave off KanagawaSome time ago, talking about fractal waves I referred to the artwork of XIX century The Great Wave off Kanagawa by japanese artist Hokusai. It was very interesting to see in old artwork selfsimilar shapes like in fractals. This artwork is of great importance to Japanese.So, it was printed on postage stamps and became inspiration for many designer works. Even more it's motif was used in Nintendo <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/g5eiw05Yi40" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2009/07/great-wave-off-kanagawa.htmltag:blogger.com,1999:blog-5301821758121626223.post-37735602914460585592009-07-05T01:37:00.001-07:002010-11-16T11:03:50.878-08:00Calendar 2010Today I would like to promote an outstanding issue, to which I attended. It's a bloc-calendar with illusions. Every page contains unique graphic work, photo or photomanipulation image with illusion or impossible figure. Arworks of such famous artists as M.C. Escher, Jos de Mey, Sandro del Prete, Istvan Orosz, Oscar Reutersvärd and many many others. Also, some my figures were printed in the <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/0AZVXHLt2Jw" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2009/07/calendar-2010.htmltag:blogger.com,1999:blog-5301821758121626223.post-47310880181497201592009-06-05T11:09:00.000-07:002009-06-05T11:49:12.798-07:00New set of fractal treesA new set of fractal trees open images by Nirolo. Nice gradients give mystical glow to trees. Probably, these trees should grow in the foresests of the elves. Curved branches look very unusual for fractals.Fairy TreeA tree of Fire and IceThe next tree is like a lightning. Branches have rough outline like real lightning. But it still variation of Pythagoras tree. The image was created by Cory Ench<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/2G0EheioyhY" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2009/06/new-set-of-fractal-trees.htmltag:blogger.com,1999:blog-5301821758121626223.post-67670427596811979472009-05-19T07:55:00.000-07:002009-05-19T10:25:36.718-07:00Impossible constructor onlineA new online constructor of impossible figures was opened as a part of community of the site Impossible World. The constructor allows to design your own impossible figures from cubes in Oscar Reutersvärd style. The figure designer is on the screenshot below.You can choose, which corners you want to cut from the cube by selecting appropriate cubes at the line of blue cubes at the top of the <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/5AHgC3-Peyo" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com0http://mathpaint.blogspot.com/2009/05/impossible-constructor-online.htmltag:blogger.com,1999:blog-5301821758121626223.post-87029804109711509022009-03-04T11:27:00.000-08:002009-03-04T11:47:54.697-08:00Cubic pyramidA nice pyramid of cubes was modeled and rendered by David Pearson (fpsurgeon). Each lower level of the pyramid consists of smaller cubes, which are four times more than above. So we see a simple but elegant fractal. This nice rendering was created as a further development of studing by author an open source program Structure Synth, which provides creating 3D structures from a set of user rules. <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/R4-Xv0blFyM" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com3http://mathpaint.blogspot.com/2009/03/cubic-pyramid.htmltag:blogger.com,1999:blog-5301821758121626223.post-27603504226395129972009-02-01T09:47:00.000-08:002009-02-01T10:39:41.152-08:00Fractals by Manny LorenzoSome time ago I've published one fractal by Manny Lorenzo in the post about Pythagoras trees. Today I would like to show some his fractals.Let start from new kinds of Pythagoras trees. He created a tree with spheres and a very strange kind of Pythagoras tree, which has infinity symbol as a base part of fractal. It looks unlike Pythagoras tree, but it is true.Also he created a set of wonderful <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/4UkIhHuoSTE" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com3http://mathpaint.blogspot.com/2009/02/fractals-by-manny-lorenzo.htmltag:blogger.com,1999:blog-5301821758121626223.post-87722069054443000712009-01-09T09:55:00.000-08:002009-01-09T10:56:14.515-08:00Escher-like mosaicsM.C. Escher is well known by his artistic regular plane divisions and artworks of impossible constructions. But he also created several artworks with irregular mosaics, which consist of shapes of various animals. Two of them you can see below. As you can see every animal in mosaics are fit all its neighbours without any gaps.Today may artists follow the way of Escher in creating complex mosaics. <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/WWSzksr91vg" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com0http://mathpaint.blogspot.com/2009/01/escher-like-mosaics.htmltag:blogger.com,1999:blog-5301821758121626223.post-2373482814155153622008-12-24T10:24:00.000-08:002008-12-24T10:50:04.176-08:00Kinetic sculptures by Haruki NakamuraLook at the photo a heart sculpture above, which is consists of closely interconnected gears. Although it seems that gears cannot move it is not. All of them can rotate around their respective centers, which your can see on a video below. Moving of gears are shown approximately on 50th second of the video but it's This kind of sculptures are called kinetic because all parts of them can move. It <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/sI2JeN_tBis" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com2http://mathpaint.blogspot.com/2008/12/kinetic-sculptures-by-haruki-nakamura.htmltag:blogger.com,1999:blog-5301821758121626223.post-28801252080377318582008-10-19T09:59:00.000-07:002008-10-20T09:58:55.197-07:00Fibonacci spiral in natureFibonacci spiral is a line, which is created by drawing arcs connecting the oppposite corners of the squares in Fibonacci tiling, which is constructed of squares whose sides are successive Fibonacci numbers in length. Fibonacci tiling Fibonacci spiralFibonacci spiral exists in many objects of wildlife. It's one ob the basic curve, which you can see in small shells of nautilus and even in spirals <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/6aird_c4qqk" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com6http://mathpaint.blogspot.com/2008/10/fibonacci-spiral-in-nature.htmltag:blogger.com,1999:blog-5301821758121626223.post-40929375548573985862008-10-12T10:44:00.000-07:002008-10-12T12:10:08.905-07:00Fractal tilingsFractal shapes can be used as tiles for filling plane. In most cases variations of the Koch snowlake are used. A simple Koch snowflake is represented to the right. To create a set of tiles, which can be used for filling whole plane, we need another variations of the snowlake which exactly match to all convexes and concaves of the first figure.Two variations of such kind of tilings were <img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/qqCQj4wyqDo" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com1http://mathpaint.blogspot.com/2008/10/fractal-tilings.htmltag:blogger.com,1999:blog-5301821758121626223.post-30750927830443716162008-09-24T04:07:00.000-07:002008-09-24T04:50:15.678-07:00Abstract creations by Vladimir BulatovVladimir Bulatov creates very complex and wonderful abstract bronze sculptures. Shapes of sculptures are based on Platonic solids, but they represent another view on these classic polyhedrons. All figures were designed using classical ideas of balance and symmetry. These abstract forms express geometric aesthetic and beauty of shapes.The photo above shows five interconnected tetrahedrons, so they<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/XC6GvxYqPE4" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com3http://mathpaint.blogspot.com/2008/09/abstract-creations-by-vladimir-bulatov.htmltag:blogger.com,1999:blog-5301821758121626223.post-51290444763192157562008-07-06T03:20:00.000-07:002008-07-06T05:01:27.631-07:00Tessellations of David BaileyM.C. Escher was the first, who used figures of birds, fishes, lizards and other animals for artistic regular plane division. Many followers then created numerous tessellation images.One of them is artist from England David Bailey. He creates his images in pen and watercolour.The main motifs of his tessellations are birds.The more complex constructions come in, when two distinct motifs are used in<img src="http://feeds.feedburner.com/~r/MathematicalPaintingsAndSculptures/~4/wE_mAD019jo" height="1" width="1" alt=""/>Vlad Alexeevhttps://plus.google.com/109898352457745591115noreply@blogger.com4http://mathpaint.blogspot.com/2008/07/tessellations-of-david-bailey.html