Structured Chaos: Using Mata and Stata to Draw Fractals
Fractals are some of the most beloved and recognizable mathematical objects studied. They have been traced as far back as Leibniz, but failed to receive rigorous examination until the mid-twentieth century with the many publications of Benoit Mandelbrot and the advent of the modern computer. The powerful programming environment of Mata, in tandem with Stata’s excellent graphics capabilities, provides a very well-suited setting for generating fractals. My talk will focus on using Mata, combined with Stata, to generate some visually recognizable fractals possibly including, but not limited to: iterated function systems (Barnsley Fern, Koch Snowflake, Gosper Island), escape-time fractals (Mandelbrot Set, Julia Sets, Burning Ship), finite subdivisions (Cantor Set, Sierpinski Triangle), Lindenmayer systems (Dragon Curve, Levy Curve), and strange attractors (Double-scroll, Rossler, Lorenz).
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