Examining the World of Fractals

1. Examining the World of Fractals Koch Examples Lorenz Attractor Graphics L-systems grammar to draw a Koch Island Graphic over three iterations, “F → F + F – F – FF + F + F – F” where degrees = 90 L-systems grammar to draw a square, “F → F + F + F + F” where degrees = 90 Iterations that use the Koch snowflake formula Torus: A doughnut-shaped surface of revolution generated by revolving a circle about an axis coplanar with the circle – A “Lorenz Attractor” design L-system Designs The Julia Set Examples Using different values for the Rayleigh number An example of Self-Similarity Example of a c ≠ 0 imaginary component that has 180º rotational symmetry L-systems example where a trunk emerges from a branch over several generations Angle 10 Axiom F F = F [ + F ] F Deterministic, context-free Lindenmayer system, or a D0L system Rule 1: a → ab Rule 2: b → a Famous example of a Julia set graphic and Cantor Dusts Adding a cursor stack to the L-system allows branching for the creation of plant-like images Myles Akeem Singleton Central Illinois Chapter National BDPA Technology Conference 2006 Los-Angeles, CA