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Author Topic: Book Recommendation/Reading order for understanding 3D fractals?  (Read 2460 times)
Description: I want to know exactly how equations translate into shapes.
0 Members and 2 Guests are viewing this topic.
Forums Newbie
Posts: 6

« on: November 23, 2014, 09:34:58 PM »


I've become fascinated with  thinking about fractals and how exactly the equations translate into shapes, especially of the 3D Mandelbulb variety, and want to find good books about it.  Plugging in variables just to see what happens is fun in its own way, but it also feels like stumbling around the dark.  I would think that having a better understanding would help me arrive at the specific shapes I want sooner, even though I'm aware that chaos isn't completely predictable!   wink

I do not have college training in mathematics.  (I did get an A in AP calc BC in High School. Unfortuately I've forgotten most of it, embarrass but am willing to re-learn what I need to in order to gain understanding.)

I'm pretty good at learning/visualizing abstract mathematical concepts, though.  So I think/hope I could learn what I need to with books alone.  I also know the (very) basic theory of 2D fractals already, I just don't understand things like the various formulas in the dropdowns, things like Mandelbox, etc...

If it's better to start with foundations in other areas before moving into fractal specific books, does anyone have a list of topics to learn, starting from the high school level?

My list would be to (re)learn:
--Basic trig (sin, cos, etc...)
--Polar coordinates
--Complex numbers
--Triplex algebra (should I learn general matrix algebra first?)

(Not sure if this is a good start or in the right order.)


I've just started this book:  http://www.amazon.com/Fractals-Space-Continuum-Michael-Peragine-ebook/dp/B0072SN3AM/ref=sr_1_1?ie=UTF8&qid=1416772158&sr=8-1&keywords=fractals+in+a+space+time+continuum
Though I'm not sure it's the best one to start with, though it seems like it's more about the world reflects 3D fractals and how they can be used as tools than basic theory for the layman.  It doesn't seem to be organized/edited well.  Anyone have opinions on it?

I haven't found much on 3D fractals specifically.  Just this:  http://www.amazon.com/Fractal-3D-Magic-Clifford-Pickover/dp/1454912634/ref=sr_1_1?ie=UTF8&qid=1416772721&sr=8-1&keywords=3d+fractals  But it doesn't mention Mandelbulb anywhere in the description, just fractal flames.

I heard "Chaos:  The Making of a New Science" is good.  Is it outdated though?  Or does that not matter for getting the foundations of 3D fractals?

(If the creators of Mandelbulb 3D and Mandelbulber could write a book on 3D fractals, that would be greeeat!)

Any other suggestions, or ideally a reading order, would be appreciated!  

« Last Edit: November 24, 2014, 12:32:41 AM by Zirngibism » Logged

Fractal Senior
Posts: 7044

formerly known as 'Trifox'

« Reply #1 on: November 24, 2014, 12:38:53 AM »

hi there, in fact i dont think a book covering the 3d formulas is available, i stil dream about writing such a book, yay, but not yet,
chaos by james gleick is just perfekt introduction to chaos theory in general, 3d fractals are mostly about rendering implicit functions,
the whole theory and mathematics basically where developped here, perhaps try mandelbox introduction by tglad

and perhaps you get some knowledge on fractals through my youtube channel wink
check out the tutorial section



divide and conquer - iterate and rule - chaos is No random!
Forums Newbie
Posts: 1

« Reply #2 on: April 01, 2017, 07:41:18 PM »

Hey folks, I am new to this forum and was looking for resources on 3d fractals. This thread
is a few years old now, are there any new books or resources out now on understanding 3d fractals?

Posts: 83

« Reply #3 on: April 02, 2017, 09:24:25 AM »

I guess in this area you don't get knowledge via books but the most common media to learn new things is via websites.

Syntopias article really helped me to understand the true meaning behind 3D fractals.
In fact the extension in it's pure definition is quite easy but the translation on the pc and mathematics is hard to obtain and this paper gives a short introduction in the problematics and also ways to do it.

If you search for a paper where also the most common 3D-fractals and it's formulas are explained ... I guess there is no such thing available since all the information is so widespread. But I would say you can also use this website itself as a 'book' since a lot of ideas originally started here and a lot of people wrote articles and linked websites to help understand their topic better.

You don't get all the usefull information by simply reading a book, in 'new' research fields like this here you have to search a lot on your own, but we are willing to provide others with thoughts and help us out because we are a community!

Some of my images: Pinterest
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