I have been sporadically blogging about Genetic Fractals and it is time to create a blog about the nuts and bolts. I will share (new) theory on fractals, genetic fractals and will give examples of their use in design and engineering and possibly other disciplines. Above all, I will post pretty pictures!
Before going much further, let me explain what genetic fractals are. A genetic fractal is a fractal made of fractals. At the root we start with a fractal tree. After a number of branchings, another fractal is grafted on the branch and this grafting can go on ad infinitum. The sprouting of a new fractal on a fractal is triggered by a genetic process, i.e. each fractal has a genetic description and where and when it sprouts is governed by a genome. I use this analogy deliberately since this is exactly how nature operates: genomes sequence genes that trigger tree-like growth in organisms. However, my purpose is not to replicate nature but to use this mechanism to generate man-made structures. These may be forms of engineering, mathematical or other technical domains.
In practice I am trying to construct fractals that a have a function (purpose) and therefore I don’t let the branching, sprouting and grafting go on for very long. That puts into question whether these are fractals at all. I use this term simply because the mechanism underlying genetic fractals are true fractal trees.
Below are a few samples of my work here.
Most tree like fractals are discrete and iterative. They are made up of straight lines and hard angles. The H-fractal is a good example.
I have developed a continuous formulation for such fractals, i.e. a fractal function that follows the same geometrical progression but that is continuous and differentiable everywhere along the paths along the fractal.
Most of my genetic fractals are in 3D. I use a raytracer (POV-Ray) to render these. The actual genetic fractals are generated by code that I have developed (Ruby). Below are two genetic fractals: the table frame and the lamp. The lamp is probably the better example as it shows three different fractals that sprout from the same origin (base, shade and light).
One of my objectives is to develop engineering paradigms using genetic fractals. I am not at a point yet where I can systematically construct useful structures but the chandelier below gives an idea of what such structures could look like. The thing to note is that the chandelier arms are fractal and that within these arms are rotating shafts that propagate the rotation from node to node until it reaches the light bulbs.
I will leave at this for now. There is some interesting maths (and ruby code) I’ll share but that isn’t stuff you can put on an about page 🙂
Please comment if you have thoughts or questions to share. Enjoy!