Simple Instructions Repeated Endlessly
Iterated Functions
Fractals
L-Systems
Mandelbrot
Julia
Algorithmic Patterns
Symmetry
Introduction
Topics that may be covered here:
- Iterated Function Systems and Fractals
- Symmetries in Space
- L Systems, Mandalas and Kolams
- Logistic Functions
- Projections
This equation will change how you see the world. It’s about the Logistic Map, bifurcation diagrams, the Mandelbrot set, animal populations, dripping faucets, neuron firing rates and more.
So let us see how we can construct this algorithmically, the different parts of it. And of course why we should bother!
What is an Iterated Function?
Well, we know what a function is don’t we? A relationship between numbers. One varies as the others, and the relationship is specified by the function. E.g. \(y = \sin(x)\).
So what is iteration then, and how do you do that to a function? It is applying the same function over and over again, by piping the results of the previous step i.e. iteration back into the function. Let us hear from Ron Eglash, the author of African Fractals: Modern Computing and Indigenous Design