This has been in the making for a while and I’ve finally taken, borrowed and stolen the time to treat genetic fractals scientifically. A paper entitled: “Derivative coordinates for analytic tree fractals and fractal engineering”. Abstract below.
I’ve submitted this to Arxiv (reference: 1501.01675). Depending on the reactions – if any – I might submit it for peer review and publication.
Either way, I had to write this as a basis for further research. Now that we have a theoretical foundation, I can build on this with shorter papers.
Derivative coordinates for analytic tree fractals and fractal engineering
8 January 2015
We introduce an alternative coordinate system based on derivative polar and spherical
coordinate functions and construct a root-to-canopy analytic formulation for tree fractals. We
develop smooth tree fractals and demonstrate the equivalence of their canopies with iterative
straight lined tree fractals. We then consider implementation and application of the analytic
formulation from a computational perspective. Finally we formulate the basis for
concatenation and composition of fractal trees as a basis for fractal engineering of which we
provide some examples.