A program for the Foenix 256 Jr. Rev B and F256 K that visualizes the Mandelbrot set and makes use of the F256 integer coprocessor. Download the two files mandelbrot.bas and mandel.prg from the release section of this repo, copy them to a F256 compatible SD card and plug that into either the SD card slot of the F256 or an SD2IEC like device. In BASIC change to the relevant device (drive 0 for the built in SD card slot or drive 1 for an SD2IEC device with device number 8) and type load "mandelbrot.bas" followed by run. This will first load the machine language part mandel.prg (which does all the mathematical heavy lifitng using fixed point arithmetic) and then start the program.

If you want to build the software yourself you will need the 64tass macro assembler and a python interpreter in your PATH. I use Ubuntu 22.04 on my development machine and I have not tested this software on any other operating system. The 64tass version available in the Ubuntu repos works for this project. Clone the repo, issue the command make publish, then copy the contents of the dist directory to a compatible SD card.

Note: The math coprocessor addresses differ between the F256 Jr. FPGA loads. You have to change the value of

• COPROC_RES in fixed_point.asm
• MUL_RES_CO_PROC in hires_base.asm
• MUL_RES in txtdraw.asm

from $DE10 to $DE04 when building for a F256 Jr. with an FPGA version below RC10. When building for a F256 Jr. with older firmware you may also have to use the version of api.asm which was current when that firmware was released. See here for information on how to update the FPGA load. The changes in the integer coprocessor happened in the bitstream RC10 for the F256 Jr. FPGA.

Some info about the picture shown above. The values used were Real part: -02.000000, Imaginary part 01.250000, zoom level 0 and iteration depth 80. These are the standard values which define the well known picture of the Mandelbrot set. Here another example.

The parameters used were: Real part 00.605b58, Imaginary part 00.aad9fc, zoom level 11, iteration depth 128.

The BASIC program allows to either generate (press G or g) a picture, load a picture (press L or l) or quitting the program. When generating a new picture the section to be visualized can be manually selected. You have to enter the real and imaginary part of the upper left corner of the desired section in the complex plane. The format used for the numbers is the same as for the C64 and X16 versions of this program. You also have to enter the zoom level, which in essence determines the size of the visualized section in the plane of complex numbers. Additionally you have to choose an iteration depth. I use typically a depth of 24. Larger values give a more precise result but lead to longer calculation times. On the other hand when zooming into the intereseting parts of the set the iteration depth also has to increase, because otherwise the potentially colourful parts simply remain black. Try for instance real part 00.4e6604 and imaginary part 00.641bc1 at a zoom level of 4 and an interation depth of 64 and calculate the picture with a lower iteration depth to see the difference. A calculation can be interrupted at any time by pressing a key. It is resumed if you press any key but n otherwise it is cancelled. After the calculation is finished the program waits for a key press and after that asks if the resulting picture should be saved or not.

Following that the program asks if you want to zoom into the set. If that question is answered with yes a rectangle is shown which can be moved with the cursor keys. Use i (zoom in) to shrink the size of this rectangle or o (zoom out) to enlarge it again. When you press Return the computational parameters are adapted to visualize the selected section and the calculation starts anew using these parameters. When you press q the values are not changed and the program returns to the main menu.

After loading a picture has been completed the program also waits for a key press. When a key is pressed you are asked if you want to zoom into the set. If that question is answered with y then you can select a section to visualize as described above. Before loading or saving a picture the drive (0, 1 or 2) to use for this operation can be changed. If one presses just return instead of selecting a number the current drive is not changed.

The project directory contains the Go source for a tool that allows you to convert a saved picture generated by F256 Mandelbrot into a PNG. Build this program on your platform of choice with go build or make f256conv. The resuting binary accepts the following CLI parameters:

Usage of ./f256_conv:
  -c string
    	File name of saved F256 CLUT (default "clut_0.dat")
  -i string
    	File name of pic to convert
  -z int
    	Zoom level (default 1)

It converts the saved file specified by the -i option into a PNG. The name of the PNG file is generated by appending .png to the input file name. The parameter -z specifies the zoom level. Valid values are 1, 2 and 3. The -c option has to specify a file which contains the so called color lookup table (or CLUT for short) that defines the colours which are used to render the picture. The file clut_0.dat in this repo contains the values of the default CLUT on my F256 machine.

The F256 version of this program needs about five minutes for the calculation of the default section at an iteration depth of 24. This is only about 60% of the runtime of the Commander X16 version (measured in the latest version of the emulator). As the F256 runs at 6.29 MHz and the X16 at 8 MHz this speedup can be clearly attributed to the F256 math coprocessor.

• We'll see