Welcome to Fractal Forums

Hello everyone,

I stuck around here after the slashdot tidal wave brought me here ;-)
(I have been experimenting with code and fractals alot, and tried my own version of the mandelbulb, which I will probably will post here one day.

Anyway, while tinkering with some fractal code, I stumbled upon a great series of images.
Here are a few for your enjoyment.

"Whale" :
(http://www.fractalforums.com/gallery/1/859_18_11_09_5_59_57.jpg)

"Witch" :
(http://www.fractalforums.com/gallery/1/859_18_11_09_6_02_42.jpg)

"Demon" :
(http://www.fractalforums.com/gallery/1/859_18_11_09_6_03_53.jpg)

Don't really know what fractal category they would belong to, since the coding was quite ad hoc  :angel1:
But I affectionately named them Doodlebrots myself, because many of them show these streaks and curves as if drawn by a fountain pen.
Has anyone seen these before, what are they ? :-)

hi there and welcome to the forum, could it be that those are iterated function systems?!?!?

Thanx !

I thought IFS would probably be the best description, but the "definition" (http://en.wikipedia.org/wiki/Iterated_function_system) didn't seem to be 100%.

I shall try to clarify more. These image were created by using the "buddhabrot" rendering technique. (is buddhabrot some sort of IFS?)
Anyway, I'm plotting orbits based on random seeds, and the color-range is defined by the escape values and plot density.
I have used various (VERY simple) non-linear functions to produce these.
And haven't even come round to tinkering with the actual parameters yet.
Most of these came out clean like this. I have found 28 so far, and as soon as I have some more time, I'll catalog, render and document them.
But I constantly get side-tracked by "ooh this could be cool" and before long my PC is hogged rendering some animation or rotation  O0

Ah - a rose by another name..
Whatever they are called, they are certainly very beautiful.
Thanks for sharing them.
:-)

welcome also to the forums... damn there are a lot of people registering now  :P

it could be represented as an IFS, but the name isn't so important :) the renders are pretty cool, i think a bit of extra contrast and zooming into the region of interest would really bring out the finer structures!

Looks like flame fractals.

you obviously have the better implementation, but is it something similar to those?

(http://fc04.deviantart.net/fs43/f/2009/129/2/a/Julia__s_almond_bread_dream_by_kram1032.png)
(http://fc06.deviantart.net/fs49/f/2009/190/1/0/battlebrot_by_kram1032.png)
(http://fc00.deviantart.net/fs40/f/2009/047/0/0/winds_of_the_phoenix_by_kram1032.png)

which exact equations did you use for them? :)

Hey cool !

Yeah that look's a lot like them !

Here is one based on the burning ship fractal:
(http://www.fractalforums.com/gallery/1/859_27_11_09_6_39_00.jpg)

The others use similar formulas, don't know which was which actually, really have to organize and catalog them.
Will do soon ! Currently a bit distracted with rendering mandelbrot heightmaps. (Also happening here I saw, very cool !)

yay, (I think,) I implemented one variant of the mandelbulb in buddhabrot style...

main problem is, due to the previous implementation, I still only get a 2D-slice of the x/y plane...

my formula is based on a certain multiplication table, which I *think*, David Makin already did use on one of his variants...

the table is:

∙	r	i	j
r	r	i	j
i	i	-j	-i
j	j	-i	-r

So, my basic 2nd grade Mandelbulb formula-set is:

w->w²+d:

x -> x² - z² + a
y -> 2xy - 2yz + b
z -> 2xz - y² + c

the pattern it gave me wasn't too interesting, though, so i played with it a bit and did three variants of a tribar set with either changing the sign in y or in z or in both.
All are nice but in my opinion, the one with z inverted (currently called "3D Space Lotus 2" - maybe a more matching name has to be found) - was the most interesting variation... so I'm still rendering that one now :)

Still catching up on past postings I have missed.  So Greetings and a belated Welcome to this particular Forum !!!     :)
And yes, these images definitely look like a mixture of buddhabrot and IFS.