These slides briefly explain how to program fractals using recursion. This slide deck focuses using a tree fractal pattern as its base and asks students to work with angles, colors and line width to create diffferent variations. If you want working code contact me.

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!

6. Tree Fractals
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7. 7
1 + 2(1/2) + 4(1/4) + 8(1/8) + ... = ∞
Length: 1
Length: 0.5
Infinite length in a finite area!

8. 8
…
Simple process
Complex result

9. 9
Recursive Definition
• Define something in terms of itself
• Tree: a trunk with two subtrees at the top

10. 10
Designing recursion
requires...
Assumption
(Leap of Faith)

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)

18. Recursive Method
Method Call

19. Angles and Length
19

20. Colors
20

21. Forests
21

22. What else?
22

23. Examples for Inspiration
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24. Golden Ratio Tree Fractal
https://www.behance.net/gallery/720515/Worlds-Largest-Fractal-Vectors

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

26. Fractal Branching Tree
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