A prime cloud, possibly also known as a primal walk, is created by starting at some point, taking a prime number, dividing it by a number, in this case 7, using the remainder to choose a direction, moving there, and repeating with the next prime number. We then colour it in based on the number of times each point is visited.
Yeah, there are 6 directions, and I mod by 7. Since we're using prime numbers, they'll never divide evenly and we will never have a remainder of 0, so we add an extra number and pretend 0 doesn't exist.
I've only seen this done twice, although I imagine there are more, and in both instances it was 2D. As far as I know this is the first time it has been done in 3D, but I could be wrong.
Senses777 has created some high resolution 2D prime clouds, as well as a program to generate prime clouds. You can visit his website here: CloudPrime
Still Image (800x600, 255KB):
primecloud.jpeg
Large Render (Requires the DivX codec) (800x600, 6.6MB):
primecloud.avi
Small Render (Requires the DivX codec) (320x240, 1.5MB):
primecloudsmall.avi
Source: source.zip
Pentium 4 (Win32 Binary): p4.zip
Athlon XP (Win32 Binary): axp.zip
x86 (Win32 Binary) (Should work on anything): x86.zip
The above programs are executed via the commandline. Takes start and end frames as arguments, or none to render all frames. You'll need to edit and recompile the source if you want a different resolution or sieve size.
Thanks to Melekor for the sieve code, Senses777 for the original program and idea, and both for helping to render the frames.
firstprime.jpg - As far as I know, this is the first 3D prime cloud ever rendered.
firstprime90.jpg - The same cloud as above but rotated 90 degrees.
primebug.jpg - Started writting filter to make the cloud look nicer. Something goes horribly wrong.
testrender.avi - First animation, to make sure it was working.
