PHYS114 Lecture Notes - Lecture 12: Sierpinski Triangle, Mandelbrot Set, Attractor
25 Dec 2018
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Document Summary
Simply defined, fractals are complicated, infinitely detailed shapes that are self-similar on all scales . A common example of a geometric fractal would be sierpinski"s gasket . A physical example would be the basins of attraction resulting from plotting the movement of a pendulum between magnets . Though the logistic bifurcation diagram is an example of a mathematical fractal, it isn"t the only one. As long as z is a complex number (a number of the form a + bi where i is based on how many time steps it takes for the equation to go above a certain value (2 timesteps, 3, ), assign each of those points a colour, and we would have created for ourselves a mandelbrot set. Mandelbrot sets, being infinite with similar but non-repeating shapes, are a common example of a fractal. The borders of the fractals is the boundary between order and chaos.
