Format fix 2006/monge/README.md + update bugs.md
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# Best Compiled Graphics
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Maurizio Monge
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Department of Mathematics
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University of Pisa
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Pisa
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Italy
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maurizio.monge at gmail dot com
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Maurizio Monge
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Italy
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<maurizio.monge at gmail dot com>
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## To build:
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Make sure you have the SDL1 (not SDL2!) development environment installed.
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```sh
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@@ -37,11 +33,16 @@ it segfaulted on his MacBook Pro with the M1 chip).
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./monge "z = 0" "z = z*z*z + c; Abs2(z) < 4"
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```
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### INABIAF - it's not a bug it's a feature! :-)
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Incorrect formulas will ungracefully crash the program.
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## Judges' remarks:
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For those who are familiar with the previous IOCCC winners, this program
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is best described as "1994/tvr meets 2001/bellard". Here you have
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mouse-manipulated fractals AND generated binary code, all in one package.
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For those who are familiar with the previous [IOCCC winners](/winners.html),
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this program is best described as "[1994/tvr](/1994/tvr/tvr.c) meets
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[2001/bellard](/2001/bellard/bellard.c)". Here you have mouse-manipulated
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fractals AND generated binary code, all in one package.
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A more appropriate award could have been "Best abuse of the
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rules", because on a non-x86-based architecture this program
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@@ -49,7 +50,7 @@ is, quite predictably, a dud.
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At the time of judging we were too mesmerized by the graphics
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to realize it; and, after all, this entry does take a special
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effort to work on both i386 and x86_64. Portable it is! :)
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effort to work on both `i386` and `x86_64`. Portable it is! :)
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## Author's remarks:
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@@ -63,103 +64,103 @@ effort to work on both i386 and x86_64. Portable it is! :)
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./monge "z = 0" "z = z*z + c; Abs2(z) < 4"
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2. Keep clicked with left or right button to zoom in or out.
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2. Keep clicking with left or right button to zoom in or out.
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3. Use the number pad '+' and '-' to increase/decrease the iteration
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count when needed.
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3. Use the number pad `+` and `-` to increase/decrease the iteration count when
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needed.
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4. Enjoy, unless you're more interested in trying to understand
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how it works. :)
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4. Enjoy, unless you're more interested in trying to understand how it works. :)
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### Introduction
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This is a fractal generator that supports custom formulas and
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real time zoom. The program needs to be run with two arguments,
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the first being a semicolon separated list of assignments to
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do once per pixel, and the second a semicolon separated list
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of assignments and conditions that will be executed (and conditions
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checked) for each iteration (up to the maximum). Using the
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left and right mouse buttons you will be able to zoom in and
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out (a la Xaos), the zooming algorithm is a bit slower than
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Xaos's but it should give slightly better results.
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This is a fractal generator that supports custom formulas and real time zoom.
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The program needs to be run with two arguments, the first being a semicolon
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separated list of assignments to do once per pixel, and the second a semicolon
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separated list of assignments and conditions that will be executed (and
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conditions checked) for each iteration (up to the maximum). Using the left and
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right mouse buttons you will be able to zoom in and out (a la
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[XaoS](https://github.com/xaos-project/XaoS)), the zooming algorithm is a bit
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slower than `XaoS`'s but it should give slightly better results.
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Formulas can use all a-z (lowercase) variables, and the special
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variables 'c' and 'i' are respectively set by default to the
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complex coordinate of the pixel and to the complex imaginary 'i'.
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Formulas can use all `a-z` (lowercase) variables, and the special
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variables `c` and `i` are respectively set by default to the
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complex coordinate of the pixel and to the complex imaginary `i`.
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All the constant numbers will be interpreted as real double
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values. Each expression must be an assignment ([variable] =
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[expr]) or a comparison with < or > ([expr1] < or > [expr2]),
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and you can add spaces as you like (as understood by the c
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function 'isspace').
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All the constant numbers will be interpreted as real double values. Each
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expression must be an assignment (`[variable] = [expr]`) or a comparison with
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`<` or `>` (`[expr1] < [expr2]` or `[expr1] > [expr2]`), and you can add spaces
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as you like (as understood by the C function `isspace()`).
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Supported operations and functions are:
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Operation | Description
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:-------- | :----------
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> `+,-,*,/` | Arithmetic operations, priority of `*`,`/` over `+,-` is respected.
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> `<,>` | 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.
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> Abs2 | Calculates the squared norm, ie: `Abs2(a+b*i)` is `(a*a+b*b)+0*i`
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> Re | Extract the real part, ie: `Re(a+b*i) is a+0*i`
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> Im | Extract the imaginary part, ie: `Im(a+b*i) is b+0*i`
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> Exp | Calculates the complex exponential, ie `Exp(a+b*i)` is
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> `e^a*(cos(b)+sin(b)*i)`
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> Ln | Calculates the principal value of the natural logarithm, ie
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> `Ln(a+b*i)` is `ln(a*a+b*b)/2` + `atan(b/a)*i`
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`+,-,*,/` | Arithmetic operations, priority of `*`,`/` over `+,-` is
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respected.
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|
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`<,>` | Compares the real parts of two complex numbers (the imaginary part
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| is ignored). Any number of conditions is allowed, the iteration
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| will just stop as soon as one of them fails.
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`Abs2` | Calculates the squared norm, i.e.: `Abs2(a+b*i)` is `(a*a+b*b)+0*i`.
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`Re` | Extract the real part, i.e.: `Re(a+b*i)` is `a+0*i`.
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`Im` | Extract the imaginary part, i.e.: `Im(a+b*i) is b+0*i`.
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`Exp` | Calculates the complex exponential, i.e. `Exp(a+b*i)` is
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| `e^a*(cos(b)+sin(b)*i)`
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Ln | Calculates the principal value of the natural logarithm, i.e.
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`Ln(a+b*i)` is `ln(a*a+b*b)/2` + `atan(b/a)*i`
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Here are a few examples of fractals you can draw:
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- Mandelbrot:
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./program "z=1" "z=z*z+c; Abs2(z)<4"
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./monge "z=1" "z=z*z+c; Abs2(z)<4"
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- Mandelbrot (return time variation):
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./program "z=c" "z=z*z+c; Abs2(z-c)>0.0001"
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./monge "z=c" "z=z*z+c; Abs2(z-c)>0.0001"
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- Julia, for `c=0.31+i*0.5`:
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./program "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z)<4"
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./monge "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z)<4"
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- Julia (return time variation), `for c=0.31+i*0.5`:
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./program "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z-c)>0.0001"
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./monge "z=c; c=0.31+i*0.5" "z=z*z+c; Abs2(z-c)>0.0001"
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- Newton, for `x^3-1`:
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./program "z=c" "p=z; z=0.6666*z+0.3333/(z*z); Abs2(p-z) > 0.001"
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./monge "z=c" "p=z; z=0.6666*z+0.3333/(z*z); Abs2(p-z) > 0.001"
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- Newton-Mandelbrot:
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./program "z=0" "p=z; z=z-(z*z*z + (c-1)*z - c)/(3*z*z+c-1); Abs2(p-z) > 0.001"
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./monge "z=0" "p=z; z=z-(z*z*z + (c-1)*z - c)/(3*z*z+c-1); Abs2(p-z) > 0.001"
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- Phoenix, Mandelbrot version:
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./program "z=0; q=0" "t=z; z=z*z+Re(c)+Im(c)*q; q=t; Abs2(z)<4"
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./monge "z=0; q=0" "t=z; z=z*z+Re(c)+Im(c)*q; q=t; Abs2(z)<4"
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- Phoenix, Julia version for `c=0.56667-i*0.5`
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- Phoenix, Julia version for `c=0.56667-i*0.5`:
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./program "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"
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./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"
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### Compilation and portability
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This program will only work on x86 (with an x87 FPU) or x86_64 machines,
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and requires the SDL library.
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but it requires the SDL library.
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Another system requirement is the mmap function (as `#define`d
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at the beginning of the program). If it is not available the
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macro M(a) will have to be replaced with a system dependent
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function that allocates readable, writable *AND* executable
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memory (it will not be possible to make this program run on
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paranoid systems (like OpenBSD IIRC) do not allow rwx memory).
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Another system requirement is the `mmap()` function (as `#define`d at the
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beginning of the program). If it is not available the macro `M(a)` will have to
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be replaced with a system dependent function that allocates readable, writable
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*AND* executable memory (it will not be possible to make this program run on
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paranoid systems (like OpenBSD IIRC) that do not allow `rwx` memory).
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However I was able to compile and make work the program under
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Linux (Debian/x86 and OpenSuSE/x86_64) and under Cygwin/x86. A
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Linux (Debian/x86 and openSUSE/x86_64) and under Cygwin/x86. A
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friend of mine was able to make it work under macOS too.
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If you want you can change the window width and height, or the default
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number of iterations (that one can be tweaked at runtime, anyway) by
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changing the definitions of W, H and I at the beginning of the code.
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changing the definitions of `W`, `H` and `I` at the beginning of the code.
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### Caveats (I just a selected few of them!)
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@@ -187,25 +188,26 @@ of how all the program works to be worked out).
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This program is a formula parser that outputs machine code that
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calculates the formula and check the given conditions. The
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machine code targets the x87 stack based FPU, and it is almost
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machine code targets the x87 stack based
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[FPU](https://en.wikipedia.org/wiki/Floating-point_unit), and it is almost
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identical for x86 and x86_64 (except for the comparison
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instructions, that have to be generated differently). The
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program keeps track of the FPU stack (the FPU has a cyclic stack
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of 8 registers) and will automatically swap to and from the
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main memory when required (ie, adds instructions to the generated
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main memory when required (i.e., adds instructions to the generated
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machine code to take care of this issue).
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The formulas are parsed recursively and machine code for the
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inner iteration loop is also generated.
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After generating the machine code, a big event loop creates (or
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zooms into) the factal executing the generated code when needed,
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zooms into) the fractal executing the generated code when needed,
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and then waits for input events.
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The zooming algorithm works by remembering for each pixel the
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floating point offset to where the value was actually calculated.
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When zooming, the best match is searched, and if the offset is
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too big (>1) the pixel is recalculated.
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too big (`>1`) the pixel is recalculated.
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## Copyright and CC BY-SA 4.0 License:
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