rmsk2 / x16_mandelbrot

A Mandelbrot set viewer that makes use of the new possibilities offered by the Commander X16

General Information

This program is a further optimzed version of my Mandelbrot set viewer for the C64 that is intended for Commander X16 (see also here on GitHub) and makes use of commander X16 features like:

• More RAM which offers the possibility to precompute more stuff
• More free zero page addresses which allow a broader use of more efficient addressing modes
• More colours to use in Hires mode (256 for the X16, 2 for the C64)
• New instructions for the 65C02 (well only stz and bra)

Currently the default section of the Mandelbrot set (see screenshot below) using the X16s full resolution of 320x240 at a depth of 24 iterations (in total 717022 iterations) is calculated in around 8 minutes and 15 seconds at about 1450 iterations/sec. The C64 version takes one hour and 15 minutes to calculate the same visualisation in a resolution of 320x200. Of course the biggest part of the speedup stems from the fact that the 65C02 in the X16 runs at 8MHz where the 6510 in a C64 is clocked at 1MHz but the X16 version is also more efficient as it only uses 84% of the clock cycles of the C64 version. The main reason for this increased efficiency is that the Commander X16 version is able to store a precomputed table (of size 128K) for 8 bit by 8 bit multiplication in RAM.

You can download a prebuilt version of the software in the release section. In order to run it you have to start the Commander X16 emulator with at least the following options -sdcard sdcard.img -rtc for all features to work. Utilize the -prg option to load the program even if it is not stored on the SD-card image or LOAD the program from SD card. Type RUN to start it. If you have a german keyboard you also may want to add -keymap de. I use ./x16emu -sdcard sdcard.img -prg mandelbr.prg -keymap de -rtc to start the emulator.

Building the software

You need the ACME macro assembler to assemble the program. A makefile is provided to simplify building the software. Under MacOS you have to set the variable MAC (use make MAC=1) when calling the makefile and you have to adapt the variables ACME and WORKDIR to reflect the situation on your machine. Under Linux the makefile should run without changes as long as ACME is in your PATH. I have tested that the software runs in the latest version of the X16 emulator (as of today: Release 46 ("Winnipeg")).

Running tests

The source code includes tests for some parts of the software. These tests make use of my 6502profiler project, which can be found here. If 6502profiler is in your PATH you can execute these tests by running make test. The test specific source code can be found in the tests directory and consists of a mixture of assembly and Lua, where the Lua scripts arrange test data and verify the expected results.

About my motivation for writing this program

Why does someone write a program (in machine language) for an 8-bit microprocessor that is nowadys only used in small embedded systems, that offers functionality which is on several levels (performance, visual appeal, ...) orders of magnitude worse than software written for the same purpose for modern systems?

The only reasons I can give are: I had fun doing it and it was nostalgic as it transported me back to the days when another 6502 system was the center of at least my (home) computing universe. The commander X16 strikes the right balance between new possibilities and a nostalgic familiarity with the Commodore family of home computers that allows all the people that grew up with these computers to now write the programs that they did not or could not write in the 80ies or 90ies.

Using the program

When you start the program you can select whether you want

1. to load a picture and its corresponding values from SD card
2. to start a new calculation using the current values but with a different iteration depth
3. to reset to the default values and start a new calculation
4. start a new calculation using the current values
5. to load calculation paramaters and start a new calculation
6. to save the current calculation parameters
7. to exit again.

An option is selected by pressing the key corresponding to the number.

When you select option 1. the picture data and its associated parameters are loaded into RAM and then shown on the screen. You can zoom into the picture by pressing F5 (see Zooming into the Mandelbrot set) below or you can look at the parameters by pressing any other key.

When you select option 2. ,3., 4. or .5 a new picture is calculated. The calculation can be interrupted at any time by pressing a key. If that key is F5 you can zoom into the Mandelbrot set (see corresponding section below). When any other key is pressed the parameters used for calculation are presented. If you then press RETURN the calculation is stopped and the program returns to the main menu. Any other key resumes the calculation.

If all calculations for a picture have been performed the program waits for a key press while showing the picture. You can either press F5 to zoom further into the set (see below) or press F7 to save the picture on SD card. If you press any other key the values used for the calculation are printed to the screen.

Zooming into the Mandelbrot set

If F5 is pressed you can select a new section of the Mandelbrot set. Use the following key commands to select the new section:

Key	Function
Cursor Keys	Move upper left corner of new section
F1	Zoom in
F3	Zoom out
F2	Abort selection
RETURN	Start calculation of new section

The cursor keys can be used to move a rectangular frame of reversed pixels over the visualization. The frame represents the currently selected new section. F1 and F3 can be used to change the size of that frame. Pressing return starts the calculation of the selected subsection.

Zooming in one level simply halves the stepping width in the complex plane in both directions. As this software uses fixed point arithmentic with 24 bits after the comma this has the consequence that the maximum zoom level is limited to 16. The theoretical maximum is 17. On zoom level 18 the stepping width in X and Y direction would become zero as the last nonzero bit would have been shifted out of the 24 bit "mantissa".

Limitations at the moment

• In the emulator loading and saving pictures only works with a mounted SD-card image. I am at the moment not sure if there is anything I can do about that.
• I have not yet tested whether my fixed point math routines are actually faster than the floating point routines in the X16s math library and if they are really faster I don't know by how much.
• Currently the 32 bit multiplication uses the text book algorithm taught at school for manual multiplication. I could test whether Karatsuba's algorithm speeds things up at least a little even in this (close to a corner) case.