Java tree fractals
- 1. Tree Fractals The Walker School APCSA 1
- 2. 2 What is a Fractal? • Geometric object • Self-similar across scale • The exhibit roughness • Recursive definition
- 3. 3 Fractal Geometry • Infinite + finite • Simple becomes complex
- 4. Where do we find fractals in nature?
- 5. Everywhere!
- 7. 7 1 + 2(1/2) + 4(1/4) + 8(1/8) + ... = ∞ Length: 1 Length: 0.5 Infinite length in a finite area!
- 9. 9 Recursive Definition • Define something in terms of itself • Tree: a trunk with two subtrees at the top
- 11. Pseudocode Algorithm • Draw the trunk • Draw the two subtrees • Go back to the base of the trunk 11
- 12. Pseudocode Algorithm • Draw the trunk • Draw the two subtrees • Go back to the base of the trunk 12
- 13. Java Code • A method that calls itself • How to stop from going forever? 13
- 14. Java Code • Base case • Recursion “bottoms out” • Must use arguments to manage this 14
- 15. 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 15
- 16. Basic Tree 16
- 17. Unit Circle 0 -90 90 180 X Y sinθ = y/1 = y cosθ = x/1 = x (x,y)(x,y)
- 20. Colors 20
- 21. Forests 21
- 22. What else? 22
- 24. Golden Ratio Tree Fractal https://www.behance.net/gallery/720515/Worlds-Largest-Fractal-Vectors
- 27. 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