Monster Tree (怪物樹)

Plane Region (Inequality)

Plane Curve (Equation)

( Mathematical software used: gnuplot )

Elder Tree (長老樹)

( Mathematical software used: gnuplot )

Wizard Tree (巫師樹)

400x295 pixels (GIF animation)

1024x755 pixels (Click on the image for a larger view.)

( Mathematical software used: UDAV )

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 )

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 )

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

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 )

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 )

Ent Warrior (樹人戰士)

( Mathematical software used: Graph )

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 )

Alien Baby Tree (外星樹寶寶)

( Mathematical software used: gnuplot )