1. HONR 300/CMSC 491 Fractals (Flake, Ch. 5)
Prof. Marie desJardins, February 14, 2011
Fractals 2/14/11

2. Happy Valentine’s Day!
Fractals 2/14/11

3. Key Ideas Self-similarity Fractal constructions Fractal widths/lengths
Cantor set
Koch curve
Peano curve
Fractal widths/lengths
Recurrence relations
Closed-form solutions
Fractal dimensions
Fractals in nature
Fractals 2/14/11

4. Hilbert Curve Another space-filling curve
Images: mathworld.com(T,L), donrelyea.com(R)
Fractals 2/14/11

5. Koch Snowflake
Same as the Koch curve but starts with an equilateral triangle
Images: ccs.neu.edu(L), commons.wikimedia.org(R)
Fractals 2/14/11

6. Sierpinski Triangle Generate by subdividing an equilateral triangle
Amazingly, you can also construct the Sierpinski triangle with the Chaos Game:
Mark the three vertices of an equilateral triangle
Mark a random point inside the triangle (p)
Pick one of the three vertices at random (v)
Mark the point halfway between p and v
Repeat until bored
This process can be used with any polygon to generate a similar fractal
Images: curvebank.calstatela.edu(L), egge.net(R)
Fractals 2/14/11

7. Mandelbrot and Julia Sets
...about which, more soon!!
Images: salvolavis.com(L), geometrian.com, nedprod.com, commons.wikimedia.org
Fractals 2/14/11