# Paper: Derivative coordinates for analytic tree fractals and fractal engineering

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

## Henk Mulder

8 January 2015

Abstract

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.

## 5 thoughts on “Paper: Derivative coordinates for analytic tree fractals and fractal engineering”

1. Well done, and congratulations! Publish or perish. And you should submit for review. I sense there’s something astonishing in this work. In Reeds Great Ship books there’s a wonder material called Hyperfiber which is strong beyond all measure. It’s strength, in part, comes from deep interactions in multiple dimensions. When it absorbs an impact the forces dissipate out through these dimensions. It’s a wild concept, and you might just be on the verge of touching it.

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• Thanks – wise words among bloggers! Yeah, hyper fiber would nicely. I am anticipating that before long 3D printing will allow us to actually fabricate such things. Genetic fractals is a little ahead of the curve and when 3D printing has caught up, I can think of some applications. Super strong suction pads together with hyper fibre will turn any kid into Spider Man.

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