Recalling derivative coordinate functions When I developed the equation for genetic fractals (paper) , I first defined a “path function”, i.e. an equation that could represent arbitrary curves. This is given as: The notation is slightly different with respect to the paper. is a derivative of the coordinate function and is a derivative of the…
I have been developing the theory and implementation of “genetic fractals” since 2010 and have often wondered what the next big step would be. You may not be familiar with genetic fractals, so here is a short definition:
Upon suggestion by one of our blog followers (thanks Ben!), I have enhanced the Genetic Fractal Explorer. There are now a lot of interesting other parameters that you can change.
The Koch curve, one of Mandelbrot’s “monsters” becomes a little more friendly when plotted using smooth (analytic) tree fractals. For details on this curve, refer to this paper.
I’d love to put the tree fractal explorer here on the blog but WordPress doesn’t allow that (for excellent reasons). Please visit the explorer here.
Previous article: Arbitrary branchings In the previous parts of this series we introduced the idea of genetic fractals, based on a simple formulation, aka the genetic equation. This equation is controlled by driver functions. Initially we started out with a driver function
Next article: plotting fractals Having plastered pretty pictures all over the internet and even having a genetic fractal in an art gallery (yes…!), the time must have come to out genetic fractals beyond sharing beautiful maths equations. So here it is, a series on constructing genetic fractals in 2 dimensions. “Why only two?”