Iteration dynamics: from convergence to fractals
Apply one rule again and again, and compare fixed points, short periods, dense long-run values, and self-repeating fractals.
Dynamical systems and chaos
4 pieces about this concept, across works, topic guides, and exam visualizations.
Topics
Works
Logistic map bifurcation diagram
Period doubling and chaotic regions of x_{n+1} = r x_n(1-x_n) as the parameter r changes.
Julia set
Iterating z to z squared plus c on the complex plane draws a fractal boundary and its self-similar structure.
Mandelbrot set and Julia set
Pick c on the Mandelbrot set and the corner draws the corresponding Julia set.