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Author Topic:  My new book is out! Exploring Scale Symmetry  (Read 131 times)

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Offline TGlad

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My new book is out! Exploring Scale Symmetry
« on: February 21, 2021, 12:05:06 PM »
Hi everyone, my new book is now out: https://www.amazon.co.uk/Exploring-Symmetry-Fractals-Dynamics-Mathematics/dp/9813278544

It's about lots of the different fractals that we have discussed and invented over the years here on FractalForums. So thanks for all the enlightening conversations and great explorations here on this site, I give a big shout out to FractalForums in the book on multiple occasions.   :thumbs: :thumbs:

It is about 3D fractals and the visual ideas behind each one. There are lots of types described, and longtimers here will recognise many of them. Such as the Mandelbox and Mandelbulbs. But also the pyramidal surface fractal, do you remember this one?:

and some much newer ones such as this very spikey looking sphere tree:

Anyway, it is a nice big visual book of fractals and scale symmetry. I hope you enjoy it! :cheer:

Linkback: https://fractalforums.org/announcements-and-news/75/my-new-book-is-out-exploring-scale-symmetry/4046/
« Last Edit: February 22, 2021, 05:33:38 AM by TGlad »

Offline mclarekin

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Re: My new book is out! Exploring Scale Symmetry
« Reply #1 on: February 22, 2021, 05:48:33 AM »
congratulations, it will be an interesting read

Offline lkmitch

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Re: My new book is out! Exploring Scale Symmetry
« Reply #2 on: February 22, 2021, 04:10:27 PM »

Offline TGlad

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Re: My new book is out! Exploring Scale Symmetry
« Reply #3 on: February 25, 2021, 08:38:35 AM »
Thanks mclarekin and lkmitch!

Here's another one from the first chapter:

You might recognise it, I called it a semi-dimensional shape because it is exactly two-and-a-half dimensional.
As 3D shapes approach 3D they fill more space, but they are in a sense less rough because they become more like a solid block with a few cracks in it.

So the best examples of fractals are (in my opinion) half way between their topological dimension and embedding dimension. The above one is a surface (topological dimension 2) in 3D (embedding dimension 3) so half way is 2.5D.

It is simple to make, you just replace every square plane

with 32 square planes of one quarter the width

The dark squares here indicate a backwards facing plane. These 'inwards' planes mean the resulting fractal is self-avoiding.

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