How would you calculate the Mandelbrot set in hardware? [closed]

Question

I'd like to build a small novelty circuit that calculates the Mandelbrot set and displays it on an array of LEDs. The minimum floating point math would not necessarily require complex numbers (just calculate \$x\$ and \$y\$ separately) and the total number of individual calculations of \$z_{n+1}=z_n^2+c\$ would be under one million, so even something as slow as ten million FLOPS per hour would be OK in this case. At this level, it looks like 16 bit math is almost enough with clever programming, 32-bits is enough to make it work. Floats rather than ints would make life a heck of a lot easier, but not required.

I believe that a Raspberry Pi would be overkill as would a high-end Arduino, so an Uno, or a Basic Stamp II with its FP coprocessor perhaps.

That exhausts my knowledge of the possibilities, but there must be other options out there. How would you go about designing a small circuit to do this? What type of circuit would you use?

Background question, and the first ever published image of the Mandelbrot set (1978):

Answer 1

I think the moset obvious solution for your requirements is using a FPGA and writing HDL code that calculates \$z_{i+1} = z_i^2 + c\$.

Answer 2

Any Cortex M4F can easily do single-precision floating point math (ie. float, not double). Here is a summary how long each instruction takes.

Example: Kinetis MK02FN128 running at 100MHz can theoretically do 100 million floating point multiplications a second.

You would write code in C with floats as you would do on a PC. Some tips. Just look for microcontrollers with Cortex M4F core or "with FPU".