Tuning to Fractals


This image is the result of progressively matching pixels with colours, by running two equivalent and parallel walks, in the 2D image space and 3D colour spectrum.

These walks happen to progress only through straight lines with either axial or diagonal orientation, occasionally switching direction and also jumping over other lines when reaching a dead end.

Starting with an empty space, the triangles and rectangles being generated are initially quite large and they delimit areas where the walk tends get trapped.

Within a delimited area, when the walk does not fill the space with a spiral or a creeping line ahead, it produces more nested rectangles and triangles, which become smaller and smaller, repeating similar patterns at different scales.

The behaviour of these walks and consequent emergence of fractals is not actually by design: it only occurs when a parameter of the generating algorithm is fine tuned to a specific range of values.

I wonder if fractals may emerge in the evolution of living organisms in a similar way, by fine tuning driven by natural selection? A particular setting enabling a small part of a genetic recipe to drive growth through a wide range of scales.

Image Licence: Public Domain (CC0).



Dimensions4,096 × 4,096