Before we look at the genetic aspect, let’s briefly look at traditional fractals. A fractal is a theoretical object that has infinitely many wiggly bits on its surface and edges. Mathematicians prefer a more rigorous definition involving non-integer dimensions and fractal enthusiasts often focus on the self-similarity property of many (but not all) fractals. This means that when you zoom in anywhere in an image of a fractal, you can see the big picture re-emerge, no matter how much you zoom in. An example of such a fractal is shown below.
Many – if not most – things in nature are approximately fractal. Often quoted examples are ferns that show repeated self similarity in their leaves and the coastline of britain that is “infinitely” wiggly. In reality these are not truly fractal. Like the image above, there is a limit how deep self similarity and wiggliness really goes in the real world.
Still, nature is a wonderful template for learning how things can be structured. When you observe a flowering plant, it is easy to see how it is composed of a root system, a stem and branch system, leaves with nerve systems and flowers which have their own architecture altogether. Yet, we know from science that a flowering plant is a single living organism with its own genome, i.e. genetic code. This is where the inspiration for genetic fractals come from: complex and composite structures that are driven by a genetic code.
The architecture of a plant – and any living organism – is that new elements grow as an extension to existing elements. When a stem is long enough, the genetic code will trigger a flower bud. When the bud evolves, it will grow stamens and pollen. Parts grow on parts. Since virtually all living organisms grown fractally, i.e. cells split and essentially form a new branch of tissue on the organism, these organisms are sequences of fractals. These are what I call genetic fractals.
Transposing this idea to engineering means growing structures that start from existing structures. The genetic code determines what that new structure will be like and when it should start “growing”. Below is an example of such a genetic fractal. A steam punk lantern. Notice how the lenses evolves in a crown before branching into twigs with wheels. In the center of it all sprouts a luminous ball.
This is not a very useful object. It isn’t even all that esthetic and I’m sure a designer could do a much better job. However, this genetic fractal conveys the idea and the concept.
As you will see elsewhere in this blog, we can do better on the usefulness and the esthetics. That is in fact, the whole purpose of this development.