Image was rendered using XaoS 3.3 working with our user formula evaluator library. Definition for this fractal can be found in [xaos_dir]/examples/Malczak/heart.xpf file, that is present in default XaoS package.
Heart fractal is a Mandelbrot type fractal. Sequence initial point can be set to 0 or to C. Sequence formula for this fractal is :
Just a quick math related explanation is needed. When we calculate n-th root of a complex number c there are exactly n distinct n-th roots of c. In expression above notation 
means that we need to calculate 6-th solution of 12-th root of a complex number c.
Other heart like fractals can be found using formulas derived from that above. Just change root order N to any other even number, and calculate its N/2 - th solution.
1 comment
Hai,
Firstly i would like to apologise to all if this message is being interpreted as spam. Frankly, i have no business connection what soever with the owner of shaamtfractal.com (refer to as shaamtfractal). I would like to appeal to any person who knew the owner of the site to contact me personally or through this blog.
I have being following shaamtfractal since i stumbled upon it 3 weeks ago from a search engine. It seems that the fractal pattern is quite unique in the sense that it doesn't match to any of the conventional formula known. I have failed to replicate it using any technique known (especially "Conflict Chamber 4", "Turning Point 2" and most of it in the gallery). I am looking from the academic's perspective and not from the artistic's perspective because to me color & shade could easily be manipulated using a wide range of graphic tools.
Some of my academic collegue gave an opinion that the image could probably being produced from a high-end graphic software but they are amazed when i showed them the enlarge original's image (7680 x 5760) because it exposed the very fine detail of the unique pattern not found in others fractal pattern. "Medussa Belt" clearly show a grow-like pattern.
I have tried in vain to get more details regarding the formula used from the site's owner but the reply is that it is an industrial secret.
BTW, i am not trying to steal any formula from the site owner but just trying to get some clue regarding the formula & technique used to produce the said images and hoping that fractal theory could made a significant leap forward.
regards,
Fractal John Doe
-Fractal Math for civilisation advancement.