Artificial DNA for Genetic Fractals

gf4

Wheels in wheels

In this blog I have referred to artificial DNA or aDNA without really explaining what I mean by this. Initially I started using this term in the context of genetic fractals which are a mathematical model of natural structures and even organisms. These genetic fractals are generated from a list of instructions that I called aDNA simply because they are the origin of these fractals in the same way that DNA is at the foundation of living organisms. In my own terminology I referred to each instruction as a gene as that seemed right.

Since then I have refined the mathematical model that includes “driver functions” that somewhat surprising look like intertwined strings, not unlike real DNA.  But that is coincidence and a just  “nice to have”.

genetic fractals

Intertwining driver functions

More interestingly,  as I develop the genetic fractals model further based in aDNA, I discover that the concept of aDNA shows surprising behaviour that may very well be found in real DNA. I’ll say upfront that I know nothing about real DNA and I’m not going to speculate whether my aDNA has anything in common in a real sense.

So what is a genetic fractal? There are many ways to describe this and looking at the images on this blog or Google will give a reasonable impression. From a geometrical perspective, a genetic fractal evolves from an arbitrary point and evolves as instructed by the aDNA. The evolution is purely geometrical and material. At each point in its evolution, a genetic fractal will take its instruction for further grows from the next gene in the aDNA. If the aDNA were infinitely long or loops back on itself, the genetic fractal would be truly fractal.  In practice they are approximately fractal, as all real world fractals are only approximately so.

So a genetic fractal is a evolving structure whose geometry flows along its axis of growth, its “branches”.

These genetic fractals are “perfect”, i.e. a genetic fractal of a rose would be a perfect rose and show no age nor deformation.  The real world is different ofcourse.

Recently I developed an extension of the genetic fractal model that would allow non geometrical information to flow along the branches of a genetic fractal. As a boring experiment I tried to create an organisation chart where the information on the hierarchical relationships between organizational layers would drive the evolution of the the genetic fractal (the organisation chart) and pass the names of the staff along as it evolved. Though not pretty (science often isn’t), it worked nicely.

3D org chart

3D Org chart: a juxtaposition of evolving geometry and information

As I observed that genetic fractal I noticed that it’s asymmetry was driven by the real world context of that organization. So here I had a perfect genetic fractal that was rendered real and imperfect by an external context.

This was modelled by a parallel aDNA string that defined the non geometrical information of the organisation chart. To avoid confusion I call this nDNA short for non geometrical aDNA. Now we have to parallel strings of aDNA and nDNA. The first defines the perfect geometrical and material structure of the genetic fractal. The second morphs it I to a real world context and gives it information meaning.

So here you have it. The genetic model of genetic fractals is getting very intriguing.  This model explains both natural perfection and real world adaptation.  The perfect aDNA stays the same over time,  including from generation to generation. The nDNA takes its influence from its context and is never the same.
I am now adjusting the mathematical model and will post it here shortly.

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10 thoughts on “Artificial DNA for Genetic Fractals

  1. Ahhhh, I needed this explanation. We joined your fabulous journey already flying, and this grounding (so to speak) helps explain where we’re going…. Not that I really cared. I lobe mystery journeys 🙂

    Hey, my learned friend, at some time in the future I might ask a favour of you. Nothing grand, certainly not challenging or particularly time-consuming, but to look over something I’m writing and see if you can package it into a neat equation. No promises. No expectations.

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