Understanding the maths

[JodyVL]

Hey guys,

As I said in this last blogpost ( http://bit.ly/ke85DQ ), I'm basically giving up on trying to understand the maths behind the Mandelbulb. But as a last desperate reach-out I'm posting here to ask, does anyone know what/where I could start in order to understand it? (Read the blogpost to see what I get so far - truly not much).

And if anyone could explain the differences between my render and the original "Cave of Lost Secrets", I'd greatly appreciate it Thanks 

[bib]

The 2 pictures are probably at the same location but they are different because of:
- different field of view
- different number of iterations
- different distance estimation method
....

[msltoe]

Jody,

Regarding the Mandelbulb's "math",twinbee's (skytopia) explanation is the best. The "hypercomplex" terminology was a way to make the formula more formal, but the concept is novel and simple. You're standing somewhere on the Earth with a latitude and longitude. Double (triple, or quadruple, etc) those two numbers and square (cube, ^4, etc) your distance to the center of the earth. Finally, add a seed , which is an x,y,z position in space. It's that simple. No quaternion math needed.

But why this formula produces such beauty vs. the hundreds tried before it is not well understood by anyone, yet.

There's also the "Mandelbox." Once again, simple formulas, but admittedly no one thought to try them out until a year ago.

-mike

[JodyVL]

bib:

Thank you... I try going to the same location and then tweak those settings a bit and see what happens.
Right now, I'm having trouble understanding how the Navigator works. I get rolling and looking, and sort-of understand sliding and walking. I -thought- I understood zooming but now since trying to get "inside" the mandelbulb, zoom has been doing a few very strange things. (I want to try and find the "Alien Ice-cream" pic, also on Skytopia). Sometimes if I focus on one area, I can zoom in pretty far. But other times, everything goes haywire, I get lots of noise and blue sky, etc...

How, for example, can one observe the center of the 'bulb and explore it?

msltoe:

Thanks for that ... The thing is, just like the 2D Mandelbrot, I felt I really should understand HOW it works before simply going in and using all the renderer's to make fractal art. Kinda would feel like I was cheating, you know? Jesse and the rest do all the hard work while I reap the rewards.

But yeah, while I certainly don't get the algebra, the general concept I have down, and I'll try and be satisfied with that ... Another reason for wanting to understand it all is that I read so many conversations here on the forums and would looove to join in, if only I understood, hehe... *sigh*

Ah well... Trial and error I suppose! Hopefully I'll get there. Thanks for your replies. Please follow my blog with Google connect (sidebar of the blog).

[Jesse]

And if anyone could explain the differences between my render and the original "Cave of Lost Secrets", I'd greatly appreciate it Thanks 

Daniel has obviously used the cosine version (CosinePow8 in m3d) for his rendering, thx i take that one

[JodyVL]

Hehe... Thanks Jesse. Nice to finally make your acquaintance. Thanks for creating such an awesome program... I truly envy your skillz, and hope that I'll be able to ask you more questions as I endeavour to learn more.

Did you know just by looking at the images, that the CosinePow8 formula was used??

As a first question (or second actually), could you help me navigate to the center of the Mandelbulb? and/or to find Daniel White's "Ice-cream From Neptune" ... I'm going to try on my own right now but it's most often a very frustrating adventure.

[Jesse]

Thx Jody, talking bout my skillz.. i got all from this forum, so i am just the author of a program but there are many more guys in here that developed this fractals and the ways to render them!

And no, i did not regocnized the specific formula type at once, just saw that something was not the way it should be and tested the cosine
after i did some changes in FOV, DE and what bib else said before 

Inside rendering is not supported by m3d because it works with distance estimates towards the set and there are no general distance estimates inside the bulbs.
But you might try other programs like Mandelbulber that has this feature, just dunno if the cosine is supported.

Cheers!

[DarkBeam]

Jody, didn't you know that Jesse can guess the parameters of every fractal just looking at it? Beginner!

[JodyVL]

Haha... Indeed DarkBean, my newbness will yet show in many various ways 

Jesse: Man! lol... If you knew all the things I've tried to get INSIDE the bulb ... hehe. But ok, good to know. So Daniel White's "Ice cream from Neptune" was definitely not done in M3D (?) ... I'll get Mandelbulber sometime soon, but I've promised my blogreaders a beginners guide to M3D so I'll keep with it for now ... I'd love to know what Johan (Mandelwerk) does though, since he uses M3D and so many of his fractal look like they're from deep inside somewhere.

(Do you think, Jesse, that inside rendering might become available in some future version?  )

Anyway, I tried again with the Cave of Lost Secrets using CosinePow8 and got this:
http://mandelubber.blogspot.com/2011/06/true-cave-of-lost-secrets-and-dream-of.html

Also please give me some critique on my second attempt at 3D Fractal art, "Dream of Death" (also on the above page) .. (I checked out CosinePow2 and found Death there  )

[DarkBeam]

I remember a beautiful render from the inside; Jesse did it with a sequence of inversions... Check his gallery