All of the posts and maths below have been superseded by a paper that presents all the research to date: Derivative coordinates for analytic tree fractals and fractal engineering
The posts are perhaps more user friendly but less formal and less accurate. I have taken care in the paper to correct errors in the formulations and introduce consistent terminology and notation.
8 January 2015
Going beyond the 3rd dimension: hyper dimensional fractals using the genetic equation.
An analysis of the genetic equation for arbitrary function: the genetic transform.
A grand overview of a closed and analytic form of genetic fractals: Genetic fractal formulation of a “Genetic Equation”.
When I started analyzing genetic fractals, I was focusing on L-system fractals, I came up with an interesting approach to create smooth fractal branches, i.e. analytic from a math’s perspective.
|from the usual angular L-system fractals||to||smooth and analytic fractals|
This led to a an analysis I reported here in a few chapters:
Also PDF-ed together here.