One of the main motivations in developing genetic fractals is in their use in systems. A fractal is a peculiar object that branches infinitely many times whilst it is still contained within a boundary. Each of the branches is connected with a root and with each other, and that makes it an interesting type of network. The genetic aspect concerns the grafting and evolving of different types of fractals, each of which may have its own function. Refer to What are genetic fractals? for a general introduction.

Beyond geometry and pretty pictures

We often think of fractals as geometrical objects but that is an unnecessary limitation. The geometry only concerns vertices and edges in some n-dimensional space. There is no reason why we would not add non-geometrical dimensions to the fractal nodes. These could be any dimension we may wish, be they colour, sound, pressure, field vectors, angular momentum etc.

Steampunk lantern

Steampunk lantern

The self similarity and the non-integer fractal dimensions will still be part of these non-geometrical fractals. For example, if we made a fractal in a colour dimension, than the branches would occupy different colour spectral lines and as we zoom in, we see repeats in these spectral bands. Calculating the fractal dimension of a colour spectrum is a little convoluted and we would be wise to retain an analogy to geometrical space to make sense of this. In practice, fractals are generated of a set of dimensions that may well include geometry, colour and other physical dimensions.

Fractals as systems

We can take a view that fractals are transport systems of dimensions where the dimensional quantity propagates through the fractal network. When we take this view, a fractal becomes a distribution system, or its reverse, a collection system. The genetic aspect of this system is that the function of the nodes evolve along the network. From that perspective, a node becomes a transfer function from the pre-node state to the post-node state. This view allows us to construct complex system functions.

GF Engineering

For test and development purposes, I have developed code in ruby and POVRay.

  • Ruby classes for modelling fractal systems: NetworkNode and Network (here)

3D printing and nanotechnology

With the advent of 3D printing technology we are presented with a new challenge: how to design 3D objects. It is straight forward to take a Lego block approach and stack simple geometrical objects along 3 or more geometrical axis. This will lead to simple forms that are variations of boxes.

We could also develop and publish parametrizable models that the user can adapt. For example, we could publish a model for a vase with parameters for its size, pearshape balance, bumps etc. But, we could not use that model for anything else.

Genetic fractals are a good candidate for 3D design for printing. It works on the bases that functionality is stackeable without needing to worry about the geometry as a first concern. The geometry can be subsequently morphed and adapted but we are starting with a functional device from the outset.

skeleton (extinct) genetic fractal

In nanotechnology we will face a similar but different problem. One of the benefits is that we can create nanosized systems. To build such systems, we need to manipulate atoms and at any serious scale, this is a challenge. The genetic fractal concept is based on a growth paradigm. Systems are grown from a root all the way up to its completion. It may well prove to be a smart approach to construction at a nanoscale, i.e. grow the system rather than compose it. This puts constraints on how you design systems and that may be where genetic fractal engineering comes into it own. Admittedly, this idea is very speculative.

So what do you think?

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