# A mathematical curiosity: A fractal tree object with branches in every dimension, up to infinity

I stumbled upon a curious mathematical beast: a fractal with infinite dimensions. I will be producing 3 dimensional renderings to get an idea what this ‘looks’  like, but let’s start with the maths. Imagine a trunk of a 1-dimensional tree, i.e. a fat line. After a while it splits into two branches in a 2-dimensional…

# Definition of geometric space around analytic fractal trees using derivative coordinate funtions

Published on arXiv, my new paper on analytic tree fractals (a.k.a. as genetic fractals). Title: Definition of geometric space around analytic fractal trees using derivative coordinate funtions Author: Henk Mulder Abstract: The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees . In…

# Fractal space

This one has been long in the making. Ever since formulating the maths of genetic fractals, I have been wondering about describing fractal space, i.e. the space around fractals. I have just submitted a paper to arXiv which is scheduled to become available in a few days. I will update this article with the link.…

# Formulation of an ellipse using derivatives coordinate functions (part 1)

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…

# The something from nothing equation

As part of the search for the answer to the ultimate question that philosophers i.e. ourselves under a starry night, we end up asking the paradoxical question: what happened before the first thing happened? Or in the present day context, what happened before the Big Bang.

# A canopy of all tree fractals

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

# Smooth Koch curve using analytic tree fractals

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.