java tree fractals

Tree Fractals

The Walker School

APCSA

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What is a Fractal?

• Geometric object

• Self-similar across scale

• The exhibit roughness

• Recursive definition

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Fractal Geometry

• Infinite + finite

• Simple becomes complex

Where do we find fractals in nature?

Everywhere!

Tree Fractals

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1 + 2(1/2) + 4(1/4) + 8(1/8) + ... = ∞

Length: 1

Length: 0.5

Infinite length in a finite area!

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…

Simple process

Complex result

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Recursive Definition

• Define something in terms of itself

• Tree: a trunk with two subtrees at the top

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Designing recursion requires...

Assumption(Leap of Faith)

Pseudocode Algorithm

• Draw the trunk

• Draw the two subtrees

• Go back to the base of the trunk

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Pseudocode Algorithm

• Draw the trunk

• Draw the two subtrees

• Go back to the base of the trunk

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Java Code

• A method that calls itself

• How to stop from going forever?

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Java Code

• Base case

• Recursion “bottoms out”

• Must use arguments to manage this

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Better Pseudocode

• To draw a tree of depth n and trunk size x:

–if depth is 1:

•Draw a trunk of length x

–else:

•Draw a trunk of length x

•Draw two trees of depth (n-1) and trunk size (x/2)

–Go back to the base of the trunk

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Basic Tree

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Unit Circle

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-90

90

180

X

Y sinθ = y/1 = y

cosθ = x/1 = x

(x,y)(x,y)

Recursive Method

Method Call

Angles and Length

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Colors

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Forests

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What else?

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Examples for Inspiration

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Golden Ratio Tree Fractal

https://www.behance.net/gallery/720515/Worlds-Largest-Fractal-Vectors

Pythagorean Tree

https://www.behance.net/gallery/720515/Worlds-Largest-Fractal-Vectors

Fractal Branching Tree

https://www.behance.net/gallery/720515/Worlds-Largest-Fractal-Vectors

Contact

If you want the Java code for some of the basic trees you can contact me at:

Thomas Cooper

The Walker School

Marietta, GA 30062

Website: http://www.thewalkerschool.org

Email: thomas.cooper@thewalkerschool.org