# Category Archives: Fractals

## Thesis Stuff

I officially submitted my Ph.D. thesis yesterday afternoon. It is a tremendous weight off of my shoulders to have that done. I’m going to take a few days off, and then I need to get cracking on a couple of … Continue reading

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## Fractals 6 Slides

On Saturday, I will be presenting some of my recent work, which extends Michel Lapidus’s theory of complex dimensions in $$\mathbb{R}^n$$ to a larger class of homogeneous metric measure spaces. In particular, I will be discussing the complex dimensions of … Continue reading

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## Seminar Talk in FRG

I gave a talk last week before the Fractal Research Group at UCR. The goal was to introduce my colleagues to the Assouad dimension, and to share some of the more interesting and/or surprising results. My notes (typos and all) … Continue reading

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## LEGO Fractals

My daughter has recently started playing with DUPLO blocks pretty consistently, which has me thinking about LEGO—the toy of my youth (and hopefully her’s in a couple of years, too!). In some ways, LEGO is an ideal medium for exploring … Continue reading

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## Newton Fractals

The question of solvability is one of the driving questions in mathematics. That is, given an equation, can it be solved? and if so, what are the solutions? There are some equations that are very easily solved. For instance, the … Continue reading

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## The Mandelbrot Set—Part VIII: Buddhabrots

The Mandelbrot Set Series: In previous discussions of the Mandelbrot set and its cousins, we have focused on how it is defined. Specifically, each member of the family of Mandelbrot sets is a collection of points that behave nicely when … Continue reading

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## The Collatz Fractal

In the past, we have spent a significant amount of time discussing the Mandelbrot set and variations thereon. We saw that each Mandelbrot, multibrot, and Julia set can be characterized as a set of complex numbers that behave “nicely” with … Continue reading

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## The Mandelbrot Set—Part VII: Multibrot Sets

The Mandelbrot Set Series: This is the seventh part in a series on Mandelbrot set fractals. In the previous post, we varied the constant term in the Mandelbrot set generating function, which gave us an infinite variety of Julia sets. … Continue reading

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## The Mandelbrot Set—Part VI: Julia Sets

The Mandelbrot Set Series: This is the sixth part in a series on Mandelbrot set fractals. Up until now, we have looked at fractals that are generated by examining the limit behaviour of points on the complex plane when a … Continue reading

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## The Mandelbrot Set—Part V: Coloring the Mandelbrot Set

The Mandelbrot Set Series: This post is the fifth in a series on the Mandelbrot set. Thus far, we have managed to define the Mandelbrot set as a collection of points or numbers on the complex plane. Every point is … Continue reading

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