Thursday, December 20, 2012

Fractal Star - Star fractal using GeoGebra

(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)

(GIF animation)

(1240x1240 pixels)

(1240x1240 pixels)

Fractal Pinwheel (GIF animation)

( Mathematical softwares used: GeoGebra, gnuplot )

Tuesday, December 4, 2012

Sierpinski Triangle Using Inequalities

(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:

( Mathematical softwares used: Graph, gnuplot )

Monday, December 3, 2012

Sierpinski Carpet Using Inequalities

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:

( Mathematical softwares used: Graph, gnuplot )

Thursday, November 15, 2012

Fat Ghost (胖鬼)

(800x800 pixels)

(800x800 pixels)

(1024x768 pixels)

( Mathematical software used: gnuplot )

Tuesday, November 13, 2012

( Mathematical software used: Graph )

Sunday, November 11, 2012

Doorway to Death (死亡走道)

Inequality Graph

Equation Graph

( Mathematical software used: gnuplot )

Friday, November 9, 2012

Ent Warrior (樹人戰士)

( Mathematical software used: Graph )

Thursday, November 8, 2012

Ghost Tree (鬼樹)

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 )

Wednesday, November 7, 2012

Little Pilots (小小飛行員)

( Mathematical software used: gnuplot )

Birdies and Doggies (小鳥與小狗)

( Mathematical software used: UDAV )

Monday, November 5, 2012

Cute Monster (可愛怪物)

( Mathematical software used: UDAV )

Sunday, November 4, 2012

Ant Alien (外星蟻人)

( Mathematical software used: gnuplot )

Face on the Wall (牆上的鬼臉)

Can you find any faces in the picture below?

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

( Mathematical software used: gnuplot )

Saturday, November 3, 2012

The Bad King and His Dogs (壞國王和他的狗)

( Mathematical software used: Graph )

Monday, October 29, 2012

Dog General (狗將軍)

( Mathematical software used: UDAV )

Sunday, October 28, 2012

Antler Pigman (鹿角豬頭人)

( Mathematical software used: Graph )

Monster Rabbit (2) (畸形怪兔 2)

( Mathematical software used: UDAV )

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