Uploaded May 2026 | Updated September 2026, 1 week ago
It's set up like a GPU is set up, with many cores, each with a long pipeline. Here there are 30 cores and a 14 long pipeline.
Each pipeline step calculates a subsequent iteration.
It is done in 15 bit precision. The precision is limited by finding |Z|^2 and similar, which is R*R+I*I, so that is like 30 bits / 2 = 15 bits roughly speaking. It does 14 iterations and that's easily extended, but the data becomes a bit garbage.
It's half a step for every tick. 2 steps probably required using integers intead of floating point.
The value 8192 is taken as 1.0 and the numbers range from -16k to 16k (or -2 to 2). To square a value like this and rescale without overflowing, it's X/8192 * X/8192 * 8192 = X^2/8192.
The simultaneous equations at each step are (kinda roughly speaking, written in combinator terms):
R*R/8192 → R
R*I/4096 → I
I*I/-8192 → R
Cr→R
Ci→I
N+(R*R+I*I (less than) ((8192*2)^2) ? 1 : 0)→N ((8192*2)^2 is 268435456, representing 2^2. Also, this is not exactly correct as I have made it, as it keeps counting and calculating instead of terminating the "loop", I just was trying to keep things compact)
It's set up like a GPU is set up, with many cores, each with a long pipeline. Here there are 30 cores and a 14 long pipeline.
Each pipeline step calculates a subsequent iteration.
It is done in 15 bit precision. The precision is limited by finding |Z|^2 and similar, which is R*R+I*I, so that is like 30 bits / 2 = 15 bits roughly speaking. It does 14 iterations and that's easily extended, but the data becomes a bit garbage.
It's half a step for every tick. 2 steps probably required using integers intead of floating point.
The value 8192 is taken as 1.0 and the numbers range from -16k to 16k (or -2 to 2). To square a value like this and rescale without overflowing, it's X/8192 * X/8192 * 8192 = X^2/8192.
The simultaneous equations at each step are (kinda roughly speaking, written in combinator terms):
R*R/8192 → R
R*I/4096 → I
I*I/-8192 → R
Cr→R
Ci→I
N+(R*R+I*I (less than) ((8192*2)^2) ? 1 : 0)→N ((8192*2)^2 is 268435456, representing 2^2. Also, this is not exactly correct as I have made it, as it keeps counting and calculating instead of terminating the "loop", I just was trying to keep things compact)
