The beauty of iterations

- Visualization of mathematical iterations.

Some odd years ago I wrote a computer program for analysing mathematical iterations in detail (bifurcations, common patterns, etc). In that process I noticed that some of the graphics where easy to the eye. Now many years later I decided to write a new app, considering only aesthetical values.

I was surprised by the variations in form and shape and the almost 3D-effect in some of the images. There are also some common patterns that can be seen in many of the images regardless of whitch equation has been used.

These images are not fractals. They are related in many ways, but there are differences too, for instance no use of complex numbers. If an equation can produce fractals it most likely generates iteratial shapes aswell. The common mechanics behind this is the iteration, where the result from previous calculation feeds the next, leading to self-organization.

I have used about 40 equations in the calculations, both one equation at a time or in combinations.

Previous images

Janne Käld 2024


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