Wednesday, January 23, 2013

Fractal Spacetree - a mothership-like fractal tree (碎形太空樹 - 像太空母艦般的碎形樹)





( Mathematical software used: GeoGebra )

Monday, January 21, 2013

Fractal Hair (2) - Super Saiyan Style Hair (碎形頭髮 2 - 超級賽亞頭)

hair = a ternary fractal tree
face = an implicit curve [f(x,y)=0]




( Mathematical software used: GeoGebra )

Saturday, January 19, 2013

Tree Star - Star in a Quinary Fractal Tree (樹星 - 五元碎形樹裡的星星)

(GIF animation)


(GIF animation)

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


(GIF animation)

(826x826 pixel²)

(826x826 pixel²)


( Mathematical software used: GeoGebra )

Friday, January 18, 2013

Fractal Hair (1) - Fractal Wig (碎形頭髮 1 - 碎形假髮)

wig = a quaternary fractal tree
face = an implicit curve [f(x,y)=0]





Example Files:


( Mathematical software used: GeoGebra )

Wednesday, January 16, 2013

Binary Fractal Tree (二元碎形樹)



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

θ12=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

θ12=90°, k1= k2=0.7







Example Files:


( Mathematical software used: GeoGebra )

Friday, January 11, 2013

Monsters Need Love Too (怪物也需要愛)

f1(x,y) > 0


fc(x,y) > 0,  c = 0.3 ~ 1


( Mathematical software used: UDAV )

Pythagoras Trees (畢達哥拉斯樹)

Two Pythagorean Tree-Fighters (top view)


Four Pythagoras Trees


Pythagoras Shoes (green)

Pythagoras Shoes (golden)


( Mathematical software used: GeoGebra )