Fun math art (pictures) - benice equation

Fractal Spacetree - a mothership-like fractal tree

2013-01-23T08:57:00.000-08:00

( Mathematical software used: GeoGebra )

Fractal Hair (2) - Super Saiyan Style Hair

2013-01-21T09:21:00.000-08:00

hair = a ternary fractal tree

face = an implicit curve [f(x,y)=0]

( Mathematical software used: GeoGebra )

Tree Star - Star in a Quinary Fractal Tree

2013-01-19T23:23:00.000-08:00

(GIF animation)

This looks like the Sierpinski pentagon without central pentagon.
(1322x1322 pixel²)

(GIF animation)

(826x826 pixel²)

( Mathematical software used: GeoGebra )

Fractal Hair (1) - Fractal Wig

2013-01-18T21:37:00.000-08:00

wig = a quaternary fractal tree

face = an implicit curve [f(x,y)=0]

Example Files:

Download the GeoGebra(.ggb) file here.

( Mathematical software used: GeoGebra )

Binary Fractal Tree

2013-01-16T06:47:00.001-08:00

θ₁=30°, θ₂=35°, k₁=0.65, k₂=0.75

θ₁=15°, θ₂=45°, k₁= k₂=0.5√2

θ₁=30°, θ₂=60°, k₁=0.65, k₂=0.75

θ₁=20°, θ₂=80°, k₁=k₂=0.65

θ₁=10°, θ₂=90°, k₁= k₂=0.5√2

θ₁=20°, θ₂=90°, k₁= k₂=0.5√2

θ₁=θ₂=45°, k₁= k₂=0.5√2

θ₁=45°, θ₂=90°, k₁=0.7, k₂=0.65

θ₁=45°, θ₂=120°, k₁=0.75, k₂=0.6

θ₁=90°, θ₂=345°, k₁= k₂=0.5√2

θ₁=θ₂=90°, k₁= k₂=0.7

Example Files:

Download the GeoGebra(.ggb) file here.

( Mathematical software used: GeoGebra )

Monsters Need Love Too

2013-01-11T23:51:00.000-08:00

f₁(x,y) > 0

f_c(x,y) > 0, c = 0.3 ~ 1

( Mathematical software used: UDAV )

Pythagoras Trees

2013-01-11T23:36:00.000-08:00

Two Pythagorean Tree-Fighters (top view)

Four Pythagoras Trees

Pythagoras Shoes (green)

Pythagoras Shoes (golden)

( Mathematical software used: GeoGebra )

Monster with Bamboo Dragonfly (Bamboo-copter)

2013-01-08T12:37:00.002-08:00

(Inequality Graph)

(Equation Graph)

( Mathematical software used: gnuplot )

Kung Fu Ghost

2013-01-08T12:30:00.000-08:00

( Mathematical software used: gnuplot )

Evil Military Counselor (邪惡軍師)

2013-01-08T12:25:00.000-08:00

( Mathematical software used: gnuplot )

Fractal Star - Star fractal using GeoGebra

2012-12-20T15:42:00.003-08:00

(GIF animation)

(1275x1275 pixels)

(GIF animation)

(1240x1240 pixels)

(GIF animation)

(1240x1240 pixels)

(GIF animation)

(1240x1240 pixels)

(GIF animation)

(1240x1240 pixels)

(GIF animation)

(1179x1179 pixels)

(GIF animation)

(1240x1240 pixels)

( Mathematical software used: GeoGebra )

Five Crescent Moons Fractal (Fractal Pinwheel)

2012-12-20T15:22:00.001-08:00

(GIF animation)

(1240x1240 pixels)

Fractal Pinwheel (GIF animation)

( Mathematical softwares used: GeoGebra, gnuplot )

Sierpinski Triangle Using Inequalities

2012-12-04T00:41:00.000-08:00

(Sierpinski triangle with hearts)

Example 1:

(iterations: 6)

(GIF animation)

gnuplot script 1:

triangle(x,y) = sqrt(3)*abs(x) - 1.5 + abs(sqrt(3)*abs(x) + 2*y - 0.5)
S0(x,y) = sqrt(3)*abs(x) - 0.75 + abs(sqrt(3)*abs(x) - 2*y - 0.25)
S1(x,y) = S0(2*x, 2*y-1) * S0(2*abs(x)-0.5*sqrt(3), 2*y+0.5)
S2(x,y) = S1(2*x, 2*y-1) * S1(2*abs(x)-0.5*sqrt(3), 2*y+0.5)
S3(x,y) = S2(2*x, 2*y-1) * S2(2*abs(x)-0.5*sqrt(3), 2*y+0.5)
S4(x,y) = S3(2*x, 2*y-1) * S3(2*abs(x)-0.5*sqrt(3), 2*y+0.5)
S5(x,y) = S4(2*x, 2*y-1) * S4(2*abs(x)-0.5*sqrt(3), 2*y+0.5)
fun(x,y) = triangle(x,y)>0 || S0(x,y)<0 || S1(x,y)<0 || S2(x,y)<0 || \
S3(x,y)<0 || S4(x,y)<0 || S5(x,y)<0 ? 0:1
set xrange [-0.5*sqrt(3):0.5*sqrt(3)]
set yrange [-0.5:1]
set pm3d map
unset colorbox
set palette model RGB defined (0 'white', 1 'red')
set size ratio -1
set samples 640
set isosamples 640
unset key
unset xtics
unset ytics
unset border
splot fun(x,y)

Example 2:

(iterations: 6)

(GIF animation)

gnuplot script 2:

S0(x,y) = sqrt(3)*abs(x) - 0.75 + abs(sqrt(3)*abs(x) - 2*y - 0.25)
S1(x,y) = S0(2*x, 2*y - 1) * S0(2*abs(x) - 0.5*sqrt(3), 2*y + 0.5)
S2(x,y) = S1(2*x, 2*y - 1) * S1(2*abs(x) - 0.5*sqrt(3), 2*y + 0.5)
S3(x,y) = S2(2*x, 2*y - 1) * S2(2*abs(x) - 0.5*sqrt(3), 2*y + 0.5)
S4(x,y) = S3(2*x, 2*y - 1) * S3(2*abs(x) - 0.5*sqrt(3), 2*y + 0.5)
S5(x,y) = S4(2*x, 2*y - 1) * S4(2*abs(x) - 0.5*sqrt(3), 2*y + 0.5)
fun(x,y) = (S0(x,y)<0 || S2(x,y)<0 || S4(x,y)<0) ? 2 : \
( (S1(x,y)<0 || S3(x,y)<0 || S5(x,y)<0) ? 1 : 0 )
set xrange [-0.5*sqrt(3):0.5*sqrt(3)]
set yrange [-0.5:1]
set pm3d map
unset colorbox
set palette model RGB defined (0 'white', 1 'green', 2 'magenta')
set size ratio -1
set samples 640
set isosamples 640
unset key
unset xtics
unset ytics
unset border
splot fun(x,y)

Graph examples:

Sierpinski triangle ( sierpinski_triangle.grf )
Sierpinski triangle with hearts ( sierpinski_triangle_hearts.grf )

( Mathematical softwares used: Graph, gnuplot )

Sierpinski Carpet Using Inequalities

2012-12-03T23:54:00.000-08:00

gnuplot script:

square(x,y) = abs(x + y) + abs(x - y) - 3
S0(x,y) = abs(x + y) + abs(x - y) - 1
f(x) = 3*abs(x) - 3
S1(x,y) = S0(3*x, f(y)) * S0(f(x), 3*y) * S0(f(x), f(y))
S2(x,y) = S1(3*x, f(y)) * S1(f(x), 3*y) * S1(f(x), f(y))
S3(x,y) = S2(3*x, f(y)) * S2(f(x), 3*y) * S2(f(x), f(y))
S4(x,y) = S3(3*x, f(y)) * S3(f(x), 3*y) * S3(f(x), f(y))
fun(x,y) = square(x,y)>0 || S0(x,y)<0 || S1(x,y)<0 || \
S2(x,y)<0 || S3(x,y)<0 || S4(x,y)<0 ? 0:1
set xrange [-1.5:1.5]
set yrange [-1.5:1.5]
set pm3d map
unset colorbox
set palette model RGB defined (0 'white', 1 'red')
set size ratio -1
set samples 640
set isosamples 640
unset key
unset xtics
unset ytics
unset border
splot fun(x,y)

Graph example:

Click here to download the example file (sierpinski_carpet.grf).

( Mathematical softwares used: Graph, gnuplot )

Fat Ghost

2012-11-15T01:49:00.000-08:00

(800x800 pixels)

(1024x768 pixels)

( Mathematical software used: gnuplot )

Masked Stranger

2012-11-13T22:02:00.000-08:00

( Mathematical software used: Graph )

Doorway to Death

2012-11-11T10:00:00.000-08:00

Inequality Graph

Equation Graph

( Mathematical software used: gnuplot )

Ent Warrior

2012-11-09T20:14:00.002-08:00

( Mathematical software used: Graph )

Ghost Tree

2012-11-08T20:35:00.000-08:00

1024x768 pixels (Click on the image for a larger view.)

This is a parameter animation for a family of inequalities of

the form f(x,y) > c, where c is the animation parameter.

( Mathematical software used: gnuplot )

Little Pilots

2012-11-07T18:29:00.001-08:00

( Mathematical software used: gnuplot )

Birdies and Doggies

2012-11-07T01:21:00.000-08:00

( Mathematical software used: UDAV )

Cute Monster

2012-11-05T22:54:00.000-08:00

( Mathematical software used: UDAV )

Ant Alien

2012-11-04T23:26:00.001-08:00

( Mathematical software used: gnuplot )

Face on the Wall

2012-11-04T12:11:00.000-08:00

Can you find any faces in the picture below?

Answer:

1248x720 pixels (Click on the image for a larger view.)

( Mathematical software used: gnuplot )

The Bad King and His Dogs

2012-11-03T07:00:00.000-07:00

( Mathematical software used: Graph )