Sometimes I pursue an idea that doesn’t immediately lead anywhere. This is one of those. I wondered what the canopies of tree fractals would look like if you plotted them next to one and other whilst varying Advertisements
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.
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).
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
Previous article: Accessory functions Next article: Going for 3D In the first 3 posts on this subject, we implemented the creation equation, added branching and dressed the resulting L-system fractals with color and width. Lovely. These fractals all have binary branchings, i.e. whenever a branch splits,
Previous article: Plotting fractals Next article: Arbitrary branchings In the previous post we created the Ruby code to implement the Genetic Equation and generated a few fractals like the one below.