Derivative coordinates for analytic tree fractals and fractal engineering

TL;DR

This paper introduces a new coordinate system for analytic tree fractals, enabling smooth and computationally efficient fractal modeling, with applications in fractal engineering and tree canopy analysis.

Contribution

It presents a novel derivative coordinate system for analytic tree fractals and demonstrates its use in smooth fractal construction and engineering applications.

Findings

Equivalent canopies between smooth and iterative fractals

Framework for fractal tree concatenation and composition

Examples demonstrating fractal engineering potential

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.