Fractal Trees in
GeoGebra
Fractal Trees in
GeoGebra
Fractal tree: Basic example
Fractal tree: Basic example
Fractal tree: Basic example
- Create segment and two branches
- Create a new tool
- Iterate
GeoGebra 5 Classic
Desktop
GeoGebra
GeoGebra 5 Classic
Desktop
GeoGebra Classic
Online
GeoGebra
😃
👈
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 1
Create segment and two branches
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 2
Create new tool
Step 3
Iterate
Step 3
IterationList()
Iterate
Flatten()
Zip()
Step 3
IterationList()
Iterate
Flatten()
Zip()
Main command
Auxiliar commands
\(\left.\right\}\)
Step 3
Iterate
IterationList(Flatten(Zip(Grow(s), s, level)), level, {{f}}, 8)
Step 3
Iterate
Fractal tree: Commands
IterationList(Flatten(Zip(Grow(s), s, level)), level, {{f}}, 8)
Fractal tree: Commands
IterationList( Flatten( Â Zip(Grow(s), s, level) Â ), level, {{f}}, 8 )
Fractal tree: Commands
IterationList( Flatten( Â Zip(Grow(s), s, level) Â ), level, {{f}}, 8 )
{{a, b, c}, {x, y, z}}
Creates a list of branches
Fractal tree: Commands
IterationList( Flatten( Â Zip(Grow(s), s, level) Â ), level, {{f}}, 8 )
{{a, b, c}, {x, y, z}}
Flattens list to one list
{a, b, c, x, y, z}
Fractal tree: Commands
\(\left.\right\}\)
Expression
that defines the tree
Counts
Start
value
Variable
IterationList( Flatten( Â Zip(Grow(s), s, level) Â ), level, {{f}}, 8 )
Fractal tree: Basic example
Fractal tree: Basic example
we can change color and thickness
Fractal tree: Using randomness
Fractal tree: Using randomness
Branches:
Rotation + Dilatation
Fractal tree: Using randomness
Dilate(Rotate(A, α, B), s1, B)
Dilate(Rotate(A, β, B), s2, B)
Branch 1:
Branch 2:
Note:Â A and B are the endpoints of the segment.
Fractal tree: Using randomness
Dilate(Rotate(A, α, B), s1, B)
Dilate(Rotate(A, β, B), s2, B)
Fractal tree: Using randomness
Dilate(Rotate(A, 5Ï€/4, B), 0.75, B)
Dilate(Rotate(A, 3Ï€/4, B), 0.75, B)
Branch 1:
Branch 2:
Fractal tree: Using randomness
Dilate(Rotate(A,5Ï€/4, B),0.75,B)
Dilate(Rotate(A,3Ï€/4, B),0.75, B)
Branch 1:
Branch 2:
π + random() * π/4
0.5 + 0.5 * random()
π - random() * π/4
0.5 + 0.5 * random()
Fractal tree: Using randomness
Fractal tree: Using randomness
ListOutPut
{Segment(B, C), Segment(B, D)}
Fractal tree: Using randomness
ListOutPut
{Segment(B, C), Segment(B, D), <S>}
If(random() > 0.7, Segment(B, E), Segment(B, B))
π + π/8 + random() * π/4
0.5 + 0.5 * random()
Rotate:
Dilate:
with respect of point B
Fractal tree: Using randomness
ListOutPut
{Segment(B, C), Segment(B, D), <S>}
Segment of
length 0
If(random() > 0.7, Segment(B, E), Segment(B, B))
Fractal tree: Using randomness
Fractal tree: Using randomness
- Create segment and branches
- Create a new tool
- Iterate
Fractal trees
By Juan Carlos Ponce Campuzano
Fractal trees
- 159