Genetic fractals…

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Let me take you for a tour in my laboratory, which happens to be located in the recesses of a confused mind. If you feel nausea anytime, please step aside, take a few deep breaths and continue the tour. We’ll wait. In any case, I blame David Yerle for waking up this monster that was sleeping quietly at my feet. In fairness, I brought it on myself with yesterdays post.

Immediately past the entrance there is a door marked “quiet”. This is where I meditate. I find that I get most of my thinking done when I’m not thinking. Creativity is most fertile in the emptiest of spaces and it fears nothing more than concentration, work and activity. So, when I’m very busy, I go here and put my legs up.

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Don’t look through the door on the right as it’s a huge and embarrassing mess. There is some unfinished mathematics on the work bench. Every time I look at it, it stares back at me with these big puppy eyes. A diffusion equation is lying on its back. I promised to invert to so that it could rebuild life, rather than decay it but as soon as I started to take it apart, I got lost. What a mess!

In the corner is a bin full of equal signs. The equations I ripped them out of, roll their eyes every time I look. ‘Happy now?’, they glare at me. They are completely paralysed without the equal sign so I’m not scared, just a bit concerned.

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On a shelf there is also a cornucopia. It served as a model for the infinite source that has created all there is. Oddly enough, it seems to protrude from another space and although it can’t be otherwise, my sceptical brain doesn’t quite buy it. Deepak Chopra said he was interested but he’s not getting it.

Let me just open the window of this room, it needs a bit of fresh air. There, that’s better. Let’s move on to the big room at the end of the corridor. “Genetic Fractals’’ it says.

We’ll skip the introductions. Mandelbrot, fractal ferns, trees, you’ve seen this and I know you have better things to do than to look at stuff you can find on Google image. Here are a bunch of genetic fractals. Feel free to touch, that’s what it’s for, you quickly get the idea.

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I have to admit that these genetic fractals started life in the mathematics lab we saw earlier. The idea is to grow complex and useful structures from a simple genetic code. The examples here are of an engineered nature. They are not all very useful but with a bit of effort they can evolve to something useful like the chairs or the windows and they are all grown from a simple genetic code.

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But genetic fractals are not just objects, they are everywhere. They are in van Gogh’s paintings and other works of genius. Here is some fractal prose.

He is in love

A man in a pair of worn trousers considered his options as he experienced a deep longing for the librarian at the university.

He was at least ten years older and judging by the state of his jeans, it wasn’t obvious that his feelings for the quiet girl at the library counter would be reciprocated. “Who ever loved that loved not at first sight?” he sighed, quoting from Shakespeare.

This is normally where nausea sets in, so let’s catch our breath for a moment. What’s that? Oh sure, no problem, we can stop the tour here.

……

I have no idea where genetic fractals will take me. As evidenced by nature and the universe, all that is around us is a fractal branch on the tree of causality that started nearly 14 billion years ago. Everywhere we look, patterns emerge and re-emerge and repeat themselves ad infinitum.

Sometimes I’m interested in the fundamental mechanism of genetic fractals in my pursuit to understand what is behind all of this. Other times, I’m just having fun following this path to see where this takes me, like a walk in an undiscovered forest. Will there be a lake for skinny dipping or will I stumble into a jagged rock face?

Who knows. I’m sure of that.

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9 thoughts on “Genetic fractals…

    1. Sure 🙂 Each of these genetic fractals are defined by a “genome”, i.e. a string of numbers that tells them how to grow, what materials to use, how many branches, what the conditions are for activating other parts of the genome etc. The simple chair for example has 3 legs and after they have grown 3 segments they activate the seat section and branch off to the back structure and so on.

      The idea is that you can genetically manipulate these things by replacing or changing parts of its genome and change a lightbulb for a feather boa, or a steel girder for a bamboo stick.

      The prose example is more conceptual. Terms loosely evolve into more expressive versions of themselves but the idea is the same.
      [closet geek]

      1. That’s really great! I love the idea of genetic manipulation in this concept. And you see this ‘activating genes’ as something akin to epigenetics, or should I think along the lines of foetal development?

      2. Actually, foetal development is not a good analogy because it involves epigenetics…I was thinking about some natural growth process or something that can be switched on and off. If that makes any sense. Sometimes I really would like to speak maths! 😉

      3. I’d use the word evolutionary. These designs evolve and adapt to their environment. I imagine devices that evolve to become useful. If one day I have nothing better to do, I’d run these through a 3D printer and actually make them real.For now, they are mostly in my mind 🙂

      4. Lol, that was the word I was trying to avoid because it implies interaction with the outside world. How would a genetic fractal do that?
        Yes, they would be great to run through a 3D printer! 🙂

      5. It’s a good point. Think of genetic fractals nearest cousins: living things. Coral reefs mould around their environment as part of their genetic instructions. At an evolutionary level species change from generation to generation and are subject to selection.

        Genetic fractals can do the same thing: adapt and evolve. These genetic fractals here are “living” in a mathematical space so adaptation, evolution and selection are easily achieved within that mathematical space.

        Once I print them, they would need to be equiped with ‘senses’ and a evolutionary selection mechanism would have to be added.

        For now, it’s easier to keep this in a mathematical world 🙂

  1. I can’t believe I missed this! So all of these images were generated with genetic fractals? Also the prose? How? I am extremely curious. Also, I would love to see the equations governing this (or the source code, since I’m guessing you’re programming this, more than doing math). I got the main idea from your answer the other day, but the details still elude me…

    1. The prose was a manual and creative attempt at showing the process of fractal expansion and how detail and complexity gets added as the fractal grows. I delighted you picked that up as I wasn’t sure it was evident after I posted it.

      Indeed, these are computer programs that implement the genetic fractal mechanics. First the genome gets read. Each gene then determines how many segment a branch will grow, how it bends or twists and whether it grows or shrinks. It also contains the condition for determining when to branch and how or whether another gene needs to be triggered, i.e. a new element added to the fractal. This gives me a set of coordinates and element types which I run through a raytracer (POVRAY) which substitutes the straight line segments for textured objects which are sized and directed as implied by the coordinates.

      The original program is in PHP and I spent a lot of time getting the 3D spherical transformations right. Thank goodness I understand a bit of maths :). I started porting this to ruby so I could add a GUI, but I didn’t make much progress yet.

      Since we ‘spoke’ last time, I’ve gone back to basics to reformulate the maths to make it more analytical rather than discrete. Not an easy challenge but a lot of fun.

      These genetic fractals are highly conceptual. Once you get the notion that they can create components (blocks of genes) that you can re-use elsewhere in a larger fractal, you can see that the applications are (should be) limitless. It is not limited to static objects but can used to build dynamical structures where the dynamics are transferred from node to node (example here: https://geneticfractals.files.wordpress.com/2013/05/genetic-fractal-engineering.gif – animated gif, give it a sec to load). A node then becomes a transfer function and it blows my mind to think what that means.

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