Author:

• Name: Maurizio Monge
  Location: IT - Italian Republic (Italy)

To build:

Make sure you have the SDL1 (not SDL2!) development environment installed.

    make

There is alternate version that lets you redefine the width and height and number of iterations to use. See Alternate code below.

Bugs and (Mis)features:

The current status of this entry is:

STATUS: doesn’t work with some platforms - please help us fix it
STATUS: INABIAF - please DO NOT fix

For more detailed information see 2006/monge in bugs.html.

To use:

    ./monge expression ...

Incorrect formulas will ungracefully crash the program.

Try:

    ./try.sh

Alternate code:

This alternate code lets you specify the width and height of the image as well as the number of iterations to perform.

Alternate build:

To use the default values, the same as monge.c, just do:

    make alt

But if you wish to actually make use of it you will want to redefine one or more of the variables W, H and I. The defaults are (respectively) 400, 300 and \128. If you wish to change the image size to 500x500 but keep the iterations the same then do:

    make clobber WIDTH=500 HEIGHT=500 alt

If you wish to keep the dimensions the same but change the iterations to 512:

    make clobber ITERATIONS=512 alt

If you specify a value less than 1 for any of these it sets it back to the default. The value 1 was selected arbitrarily and such a small number as 1 will not do anything useful but as long as it’s at least 1 it’ll not be redefined. It does not try taking care of overflows but such large values would be impractical anyway.

Alternate use:

Use monge.alt exactly as you would monge above.

Alternate try:

    ./try.alt.sh

Judges’ remarks:

For those who are familiar with the previous IOCCC entries, this program is best described as “1994/tvr meets 2001/bellard”. Here you have mouse-manipulated fractals AND generated binary code, all in one package.

A more appropriate award could have been “Best abuse of the rules”, because on a non-x86-based architecture this program is, quite predictably, a dud.

At the time of judging we were too mesmerized by the graphics to realize it; and, after all, this entry does take a special effort to work on both i386 and x86_64. Portable it is! :)

Author’s remarks:

For the impatient:

0. Compile using the Makefile, or just run:

    gcc monge.c -o monge -O3 `sdl-config --libs --cflags`

1. Run:

    ./monge "z = 0" "z = z*z + c; Abs2(z) < 4"

2. Keep clicking with left or right button to zoom in or out.

3. Use the number pad + and - to increase/decrease the iteration count when needed.

4. Enjoy, unless you’re more interested in trying to understand how it works. :)

Introduction

This is a fractal generator that supports custom formulas and real time zoom. The program needs to be run with two arguments, the first being a semicolon separated list of assignments to do once per pixel, and the second a semicolon separated list of assignments and conditions that will be executed (and conditions checked) for each iteration (up to the maximum). Using the left and right mouse buttons you will be able to zoom in and out (a la XaoS project), the zooming algorithm is a bit slower than XaoS’s but it should give slightly better results.

Formulas can use all a-z (lowercase) variables, and the special variables c and i are respectively set by default to the complex coordinate of the pixel and to the complex imaginary i.

All the constant numbers will be interpreted as real double values. Each expression must be an assignment ([variable] = [expr]) or a comparison with < or > ([expr1] < [expr2] or [expr1] > [expr2]), and you can add spaces as you like (as understood by the C function isspace()).

Supported operations and functions are:

• +, -, *, /
  • Arithmetic operations, priority of * , / over +,- is respected.
• <,>
  • Compares the real parts of two complex numbers (the imaginary part is ignored). Any number of conditions is allowed, the iteration will just stop as soon as one of them fails.
• Abs2
  • Calculates the squared norm, i.e.: Abs2(a+b*i) is (a*a+b*b)+0*i.
• Re
  • Extract the real part, i.e.: Re(a+b*i) is a+0*i.
• Im
  • Extract the imaginary part, i.e.: Im(a+b*i) isb+0*i.
• Exp
  • Calculates the complex exponential, i.e. Exp(a+b*i) is e^a*(cos(b)+sin(b)*i).
• Ln
  • Calculates the principal value of the natural logarithm i.e. Ln(a+b*i) is ln(a*a+b*b)/2 + atan(b/a)*i.

Here are a few examples of fractals you can draw:

• Mandelbrot:

    ./monge "z=1" "z=z*z+c; Abs2(z)<4"

• Mandelbrot (return time variation):

    ./monge "z=c" "z=z*z+c; Abs2(z-c)>0.0001"

• Julia, for c=0.31+i*0.5:

    ./monge "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z)<4"

• Julia (return time variation), for c=0.31+i*0.5:

    ./monge "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z-c)>0.0001"

• Newton, for x^3-1:

    ./monge "z=c" "p=z; z=0.6666*z+0.3333/(z*z); Abs2(p-z) > 0.001"

• Newton-Mandelbrot:

    ./monge "z=0" "p=z; z=z-(z*z*z + (c-1)*z - c)/(3*z*z+c-1); Abs2(p-z) > 0.001"

• Phoenix, Mandelbrot version:

    ./monge "z=0; q=0" "t=z; z=z*z+Re(c)+Im(c)*q; q=t; Abs2(z)<4"

• Phoenix, Julia version for c=0.56667-i*0.5:

    ./monge "z=c; c=0.56667-i*0.5; q=0" "t=z; z=z*z+Re(c)+Im(c)*q; q=t; Abs2(z)<4"

Compilation and portability

This program will only work on x86 (with an x87 FPU) or x86_64 machines, but it requires the SDL library.

Another system requirement is the mmap(2) function (as #defined at the beginning of the program). If it is not available the macro M(a) will have to be replaced with a system dependent function that allocates readable, writable AND executable memory (it will not be possible to make this program run on paranoid systems (like OpenBSD IIRC) that do not allow rwx memory).

However I was able to compile and make work the program under Linux (Debian/x86 and openSUSE/x86_64) and under Cygwin/x86. A friend of mine was able to make it work under macOS too.

If you want you can change the window width and height, or the default number of iterations (that one can be tweaked at runtime, anyway) by changing the definitions of W, H and I at the beginning of the code.

Caveats (I just a selected few of them!)

• The zooming speed depends on the speed of the computer.
• Incorrect formulas will ungracefully crash the program.
• Many SDL identifiers are hardcoded as number, this is safe up to ABI incompatibility.
• Better optimization could be done treating known real numbers as just one double, instead of adding a 0 imaginary part to treat them as complex numbers.
• There should be some way to switch from Mandelbrot to Julia with chosen parameter.

NOTICE to those who wish for a greater challenge:

If you want a greater challenge, don’t read any further: just try to understand the program via the source.

If you get stuck, come back and read below for additional hints and information.

Obfuscation

Sure, I don’t want to deprive you of the pleasure of digging into the infernal mess created by my corrupted mind (writing this remark I noticed that I was ending sentences with ‘;’ instead of with ‘.’, and I worried for my sanity), but just in case…

I used many obfuscation techniques, including a few ones that are different from the tricks used in most common IOCCC program (more ‘high level’, in the sense that they require an understanding of how all the program works to be worked out).

This program is a formula parser that outputs machine code that calculates the formula and check the given conditions. The machine code targets the x87 stack based FPU, and it is almost identical for x86 and x86_64 (except for the comparison instructions, that have to be generated differently). The program keeps track of the FPU stack (the FPU has a cyclic stack of 8 registers) and will automatically swap to and from the main memory when required (i.e., adds instructions to the generated machine code to take care of this issue).

The formulas are parsed recursively and machine code for the inner iteration loop is also generated.

After generating the machine code, a big event loop creates (or zooms into) the fractal executing the generated code when needed, and then waits for input events.

The zooming algorithm works by remembering for each pixel the floating point offset to where the value was actually calculated. When zooming, the best match is searched, and if the offset is too big (>1) the pixel is recalculated.

Primary files

• monge.c - entry source code
• Makefile - entry Makefile
• monge.alt.c - alternate source code
• monge.orig.c - original source code
• try.alt.sh - script to try alternate code
• try.sh - script to try entry

Secondary files

• 2006_monge.tar.bz2 - download entry tarball
• README.md - markdown source for this web page
• .entry.json - entry summary and manifest in JSON
• .gitignore - list of files that should not be committed under git
• .path - directory path from top level directory
• index.html - this web page

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