How to write a book about the Mandelbrot set

[claude]

Hi everyone,

I've sorta found myself starting to write a book about the Mandelbrot set that aims to bridge the gap between popular science books that give a cursory overview of many different fractals, and hardcore mathematical theses that are incomprehensible to mortals.  Such a book might already exist, but I haven't found one yet - suggestions welcome!

The general narrative through the book starts from scratch in how to write a program to generate images of the Mandelbrot set, and will hopefully eventually progress to cover techniques like parallel, concurrent and GPU programming, interactive user interfaces, animation techniques, interleaved with mathematical bits that show the rich mathematical structure of the set and how to find regions of interest in a more analytical way than exploration by eye alone.

I typed up the page images linked from [1] into [2] and exported the repository [3] to a pdf [4], and I already had some typed up notes on bond point location [5] and perturbation techniques [6].  I've never written a book before, it's quite a learning process, and I'll probably include some meta-chapters about the technical side of writing the book itself.  Naturally I'll incorporate most of my blog posts [7] too.

[1] http://mathr.co.uk/blog/2014-03-06_mandelbrot_notebook.html
[2] http://mathr.co.uk/mandelbrot/notebook.pdf
[3] https://gitorious.org/maximus/book
[3] http://code.mathr.co.uk/book
[4] http://mathr.co.uk/mandelbrot/book-draft-20131224.pdf
[5] http://mathr.co.uk/mandelbrot/bonds.pdf
[6] http://mathr.co.uk/mandelbrot/perturbation.pdf
[7] http://mathr.co.uk/blog/mandelbrot.html

Thanks for reading, suggestions on any aspect of this project will be gratefully received.

[knighty]

 

Just keep in mind that what is obvious for you won't be necessarily obvious for the reader. I gess that's why most books are so thick.

[cKleinhuis]

i have such a project in my mind since ages, my aim would be to cover not only the mandelbrot but fractal image generation techniques, especially those "newer" ones, like flame fractals (extension of iterated function systems), 3d variants ( mandelbulb + mandelbox ), but most certainly i would like to talk about hybridisation  techniques, perhaps we might join forces

a book that i still find awesomely interesting, well written and full of knowledge is "Chaos" by "James Gleick" it is from 1982 i think, but it still holds true!

[claude]

Just keep in mind that what is obvious for you won't be necessarily obvious for the reader. I gess that's why most books are so thick.

True, and it's hard to balance the obviousness for different levels of readers - once I've got more written the "fun" stuff of organising into more-standalone chapters will start...

[claude]

i have such a project in my mind since ages, my aim would be to cover not only the mandelbrot but fractal image generation techniques, especially those "newer" ones, like flame fractals (extension of iterated function systems), 3d variants ( mandelbulb + mandelbox ), but most certainly i would like to talk about hybridisation  techniques, perhaps we might join forces

Cool idea - it's just the getting started and finding time to continue regularly that is the hard part - for me it's like there's so much to cover it's hard to know where to start

I'll be sticking quite closely to just the quadratic Mandelbrot set, with occasional Newton fractal bits (because Newton's method is so useful in various algorithms).  I probably won't even cover Julia sets in any great depth either.  And still I anticipate it will be quite long!

[cKleinhuis]

you cant leave out julia sets

for once it is a historical connection, julia sets where there before, and the mandelbrot set is basically just a map of all julia seeds that produce a connected result

so, its quite important to include the connection between julia and mandelbrot, i am going to cover this in one of my following youtube shows!

when you want to deeply cover the mandelbrot set, be sure to include an analytical part about it as well, how the derivative can be used to obtain a distance estimation

[claude]

you cant leave out julia sets

True!  I'll get around to them at some point

Not written anything about them so far though.  Just working towards interior coordinates and interior distance estimation at the moment, before moving on to more abstract things like internal and external angles and rays

Here's the current (very scrappy) draft: http://mathr.co.uk/mandelbrot/book-draft-2014-04-25-web.pdf (3.3MB)