fractal image #5 - heart fractal
This time i want to share with my quite new discovery.
I've called this fractal 'heart fractal'. As can be seen in image above, this name is quite obvious.
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.
over 1 year ago Fractal John Doe #0
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.