390 Smerity-Mandelbrot
390 : Smerity-Mandelbrot
- Author: Stephen Merity
- Description: An interactive fixed-point Mandelbrot iterator with a sequential (bit-serial) multiplier. Tested on iCEBreaker FPGA V1.1a.
- GitHub repository
- Open in 3D viewer
- Clock: 10000000 Hz
How it works
A fixed-point Mandelbrot renderer.
The chip walks a 320×240 raster; for each pixel it iterates z = z² + c in Q4.28 (32-bit signed) and outputs the iteration count (0 = "in the set").
To keep the area small it uses a single sequential bit serial shift-add multiplier, shared across the three products per iteration.
The host owns the view, the chip is a pure pixel engine.
- Input — view packet. The host sends the top-left corner
c0and the step (complex units per pixel) as three signed Q4.28 fields, plus a 1-byte maxit (runtime iteration limit) — 13 bytes total, MSB-first onui_in, framed byparam_frameand strobed byparam_valid. The chip latches it and commits at the nextframe_start, so a view (or maxit) change never tears a frame. A coordinate generator (DDA, pure adds) walkscacross the frame. A default full view and maxit=100 are loaded on reset. - Output — pixel stream.
uo_outcarries the pixel value;pix_valid,frame_start, andline_endstrobes (on the bidir pins) delimit the stream. Because the markers are their own wires, pixel values use the full range.
The whole datapath is reset by rst_n (no power-on register state).
How to test
The chip free-runs, rendering the current view forever. On a TinyTapeout demo
board, bridge the parallel pins to USB with an RP2040 PIO program: emit 0xFF on
frame_start, 0xFE on line_end, and uo_out on pix_valid. Since pixel
values stay below 0xFE, this reproduces a simple framed byte stream that a
desktop viewer can draw directly (map the iteration count to a grayscale/colour
palette; 0 = in-set = dark).
To change the view (zoom/pan/iterations), compute c0, step, and maxit on the
host and send the 13-byte packet over ui_in with the param_valid /
param_frame handshake.
The included cocotb test resets the design, checks the bidirectional directions, and verifies the first pixels of the default view against a bit-exact reference.
External hardware
- An RP2040 (the TinyTapeout demo board's microcontroller) to bridge the parallel pixel bus + view-packet bus to USB
- A host running a small viewer (pygame) to display the stream and compute view packets
IO
| # | Input | Output | Bidirectional |
|---|---|---|---|
| 0 | view-packet data 0 | pixel value 0 | pix_valid (out) |
| 1 | view-packet data 1 | pixel value 1 | frame_start (out) |
| 2 | view-packet data 2 | pixel value 2 | line_end (out) |
| 3 | view-packet data 3 | pixel value 3 | param_valid (in) |
| 4 | view-packet data 4 | pixel value 4 | param_frame (in) |
| 5 | view-packet data 5 | pixel value 5 | |
| 6 | view-packet data 6 | pixel value 6 | |
| 7 | view-packet data 7 | pixel value 7 |