The fractal universe in a nutshell.

 

'Fractal blossom' - digital painting George Roberts March 2024

'Tardigrade' digital painting - George Roberts March 2024

'It's life Jim but not as we know it' - digital painting George Roberts March 2024

These images were constructed and rendered using the mathematics of fractals and the excellent and powerful freeware INCENDIA and Mandelbulb 3d. Many thanks to Prof GP for recommending this software. The above images were finally composed using Affinity Photo 2 software.

All fractals show some self-similarity. If you look ever closer into the details of a fractal, you observe multiple replicas of the whole.

Fractals can often be seen in nature. A fern is a classic example, with each of the branches coming off the main stem being similar to the entire frond. They are self-similar to the original but on a smaller scale.

These self-similar patterns are the result of a simple equation or mathematical statement. You create  a fractal algorithm by repeating this equation through a feedback loop. This process is called iteration  with the results of one iteration forming the input value for the next.

The patterns created by these algorithms often have fractal dimensions that are not whole numbers. Fractal dimension is a measure of shape complexity. Fractals are also recursive irrespective of scale - repeating themselves endlessly.