## Fractal Videos

The Maths Town YouTube channel has a large collection of fractal videos. You will find some detailed information about these videos on the website.

A fresh take on the Mandelbrot Set! A new colouring technique that chooses the colour based on the angle to the nearest point in the Mandelbrot Set. Actually, this is the technique I use to shade the "3D look" you have seen in other videos, but here I've isolated the technique and used colour. Its interesting how the colour rays are attracted to the points of the shapes in this mode. We also dive deep into some "Mandelbrot crack" here, so you might wish to watch it after the children have gone to bed.

A colour scheme that I have used before applied to a new fractal. This is a 3rd Power Mandelbrot zoom (z = z^3 + c). The third power is nice because we get some 3-way symmetry, instead of the usual 2.

The dreams video is a meditative journey into the Mandelbrot Set. This video relies on colour cycling to animate small bands of colour, creating mesmerising movement.

The happiest ultra-deep Mandelbrot ever made! An enormous amount of CPU time went into producing this Mandelbrot zoom, diving to a depth of 1.2e1077 in stunning 4k 60fps! I hope you enjoy it! I find bright and vibrant colours to be a personal challenge to create.

Many of my videos give some illusion of motion, but this video probably does that more than most. Rest assured, there is no motion but forwards, we are always zooming at same point. I had a request for some colour-cycling videos, so here it is. The colour pallette is cycling at a constant rate throughout this video. This zoom is located on the real number line

Roses Two is a relaxing Mandelbrot fractal zoom that uses an "image orbit trap" colouring technique. Here we also have a little "behind the scenes" look at how the project was built.

Tau (τ) is a mathematical constant equal to 2π. Tau is the ratio of a circle’s circumference and its radius, approximately 6.28. Actually, tau is not in popular in mathematics, the use of π is far more common. (π is the ratio of the diameter to the circumference). Here we use tau as the exponent (instead of 2) in the common Mandelbrot formula. Such use has no significant meaning other than general curiosity, but it does give us good excuse to inspect a fractal with a fractional exponent.

Set to the music of "Mars" from Gustav Holst's "The Planets". We zoom into the 5th power Mandelbrot fractal. This is part of a small series using Holst's music. I got the inspiration to do this from previous zooms where I have tried to match the time signature to the fractal's power. Very little music is written in 5:4. Holst's "Mars" is in 5:4. You may notice that this music is quite similar to parts of Star Wars, indeed, Holst was the inspiration for the Star Wars music.

Set to the music of "Mercury" from Gustav Holst's "The Planets". We zoom into the 5th power Mandelbrot fractal, with a colour scheme inspired by the planet Mercury. It's something a little different...

Explore what happens when the power of the Mandelbrot zoom is a fractional value. In this case the exponent is 2.5. The standard Mandelbrot 2, and other integer values produce similar fractals. However things start to become a little wild when we use a fractional power. (z = z^{2.5} +c)

Exploring the Mandelbrot fractal quite close to the real number line. This was the first video I have generated with a new CPU, the AMD Threadripper 1950X (16 core, 32 thread), and the speed increase is noticeable.

Can you see a teddy bear? This is a standard Mandelbrot Fractal but I have chosen a particular colour set. When the colours align in a certain way you may see a teddy bear!

Diving into the Mandelbrot fractal. There seems to be endless dinosaur fossils, at least that is what I see. What do you see?

Our first video exploring the 3rd power Mandelbrot fractal. The 3rd Power Mandelbrot is different to the normal Mandelbrot because it results in 3-way rotational symmetry, as opposed to the usual 2-way. A fractal a like to call the "Tribrot", this fractal iterates over the equation "z=z^{3}+c".

An adventure in the double spiral valley of the 4th power Mandelbrot fractal. This fractal iterates over the function "z=z^{4}+c".

Maths Town's first 4th Power Mandelbrot fractal zoom. The 4th power Mandelbrot has 4-way symmetry so things get circular more quickly, and we find minibrots easier. Instead of iterating over "z=z^{2}+c" this fractal iterates over "z=z^{4}+c".

This video is a demonstration of what happens when you increase the power of the Mandelbrot Set. The associated equation is in the lower right hand corner of the video. Integer powers give the family group of Mandelbrot shapes and are analytic. Non-integer powers are non-analytic and are full of fault lines.

This ultra-deep Mandelbrot zoom was featured on the TV show "The Big Bang Theory". Rendered in two passes, it was the deepest fractal zoom on the channel when it was released, and it has remained hugely popular.

This Mandelbrot zoom was intended to to be more a mathematical curiosity than artistic work. However, it proved to be more popular than I expected. It is a journey of infinite line work.

One of my favourite little zooms from the earlier Mandelbrot zooms on Maths Town. At about 1:40 the zoom drops into a mini-Mandelbrot and begins some very dense spirals. The spiral patterns then repeat periodically at higher symmetry. A Mandelbrot zoom that was requested by shoenborg.

Diving into the real number line in the video. This video passes quite a few minibrots on the way down. With the benefit of hind site, I think the colour scheme could be better, but it does pass through some nice geometry. At the centre of this video is the real-number line, which is part of the Mandelbrot set. All of the real numbers between -2 and 1/4 are part of the Mandelbrot set.

A Mandelbrot fractal zoom that I have rendered with a "Fire & Ice" colour scheme. This location is quite interesting because it almost never spirals! Magnification 3.5e510! This location was requested by "Mateus Machado Fotografia".

One of the early fractal zooms on the Maths Town channel. This location was requested by "Mateus Machado Fotografia". This is one of the few videos on my channel that does not finish on a mini-Mandelbrot. It is rendered using a random colour palette using "Kalles Fraktaler".

The popular 11 dimensions video was the first fractal video uploaded to the Maths Town channel. An array of beautiful colour and shape. This video finishes on the image known as "11 Dimensions"