Install
Dependencies
- pkg-config
- math
- gmp
- mpfr
- mpc
- pari
- ghci
- cairo ( and pixman )
- mandelbrot-numerics
- mandelbrot-symbolics
- openmp
shared libraries
ldd m-render
linux-vdso.so.1 => (0x00007ffcae4e7000)
libmandelbrot-graphics.so => /home/a/opt/lib/libmandelbrot-graphics.so (0x00007fb8f9a12000)
libcairo.so.2 => /usr/lib/x86_64-linux-gnu/libcairo.so.2 (0x00007fb8f96df000)
libmandelbrot-numerics.so => /home/a/opt/lib/libmandelbrot-numerics.so (0x00007fb8f94cf000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007fb8f92b2000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007fb8f8ee9000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007fb8f8bdf000)
libgomp.so.1 => /usr/lib/x86_64-linux-gnu/libgomp.so.1 (0x00007fb8f89bd000)
libpixman-1.so.0 => /usr/lib/x86_64-linux-gnu/libpixman-1.so.0 (0x00007fb8f8715000)
libfontconfig.so.1 => /usr/lib/x86_64-linux-gnu/libfontconfig.so.1 (0x00007fb8f84d1000)
libfreetype.so.6 => /usr/lib/x86_64-linux-gnu/libfreetype.so.6 (0x00007fb8f8227000)
libpng12.so.0 => /lib/x86_64-linux-gnu/libpng12.so.0 (0x00007fb8f8002000)
libxcb-shm.so.0 => /usr/lib/x86_64-linux-gnu/libxcb-shm.so.0 (0x00007fb8f7dfd000)
libxcb-render.so.0 => /usr/lib/x86_64-linux-gnu/libxcb-render.so.0 (0x00007fb8f7bf3000)
libxcb.so.1 => /usr/lib/x86_64-linux-gnu/libxcb.so.1 (0x00007fb8f79d1000)
libXrender.so.1 => /usr/lib/x86_64-linux-gnu/libXrender.so.1 (0x00007fb8f77c6000)
libX11.so.6 => /usr/lib/x86_64-linux-gnu/libX11.so.6 (0x00007fb8f748c000)
libXext.so.6 => /usr/lib/x86_64-linux-gnu/libXext.so.6 (0x00007fb8f727a000)
libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007fb8f705f000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007fb8f6e57000)
libmpc.so.3 => /usr/local/lib/libmpc.so.3 (0x00007fb8f6c3e000)
libmpfr.so.4 => /usr/local/lib/libmpfr.so.4 (0x00007fb8f69db000)
libgmp.so.10 => /usr/local/lib/libgmp.so.10 (0x00007fb8f6764000)
/lib64/ld-linux-x86-64.so.2 (0x0000564eca780000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007fb8f6560000)
libexpat.so.1 => /lib/x86_64-linux-gnu/libexpat.so.1 (0x00007fb8f6336000)
libXau.so.6 => /usr/lib/x86_64-linux-gnu/libXau.so.6 (0x00007fb8f6132000)
libXdmcp.so.6 => /usr/lib/x86_64-linux-gnu/libXdmcp.so.6 (0x00007fb8f5f2b000)
objdump -p m-render | grep NEEDED
NEEDED libmandelbrot-graphics.so
NEEDED libcairo.so.2
NEEDED libmandelbrot-numerics.so
NEEDED libpthread.so.0
NEEDED libc.so.6
objdump -p m-stretching-cusps | grep NEEDED
NEEDED libmandelbrot-graphics.so
NEEDED libcairo.so.2
NEEDED libmandelbrot-numerics.so
NEEDED libm.so.6
NEEDED libgmp.so.10
NEEDED libpthread.so.0
NEEDED libc.so.6
git
git clone https://code.mathr.co.uk/mandelbrot-graphics.git
and in the directory containing mandelbrot-graphics:
make -C mandelbrot-graphics/c/lib prefix=${HOME}/opt install
make -C mandelbrot-graphics/c/bin prefix=${HOME}/opt install
hen to run do:
export LD_LIBRARY_PATH=${HOME}/opt/lib
check :
echo $LD_LIBRARY_PATH
result :
/home/a/opt/lib
or
export PATH=${HOME}/opt/bin:${PATH}
check :
echo $PATH
To set it permanently change file :
update
git
From console opened in the mandelbrot-graphics directory :
git pull
If you made some local changes you can undu them :
git checkout -f
then
git pull
Now install again
How to use it ?
code
- C source should *only* have #include <mandelbrot-numerics.h>
- compile and link with pkg-config: see mandelbrot-numerics/c/bin/Makefile for an example
- quickest way to get started is to just put your file in mandelbrot-numerics/c/bin and run make
procedures
m_d_transform *rect = m_d_transform_rectangular(w, h, c, r); //
where :
- w = width in pixels
- h = height in pixels
- c = center of the image ( complex number )
- r = radius of the image ( double number
binaries
List :
~/mandelbrot-graphics/c/bin$ ls -1a *.c
result :
m-cardioid-warping.c
m-render.c
m-subwake-diagram-b.c
m-dense-misiurewicz.c
m-stretching-cusps.c
m-subwake-diagram-c.c
m-feigenbaum-zoom.c
m-subwake-diagram-a.c
m-furcation-rainbow
For non-real C you can plot all the limit-cycle Z on one image, chances of overlap are small. You can colour according to the position along the path. In attached I have coloured using hue red at roots, going through yellow towards the next bond point in a straight line through the interior coordinate space (interior coordinate is derivative of limit cycle). I have just plotted points, so there are gaps. Perhaps it could be improved by drawing line segments between Z values, but I'm not 100% sure if the first Z value found will always correspond to the same logical line, and keeping track of a changing number of "previous Z" values isn't too fun either. Claude[3]
Run:
/m-furcation-rainbow 13.png "1/3" "1/3" "1/3"
m-dense-misiurewicz
Program is based on m-render.c from mandelbrot-graphics.
It draws series of png images
cardioid warping
The exterior of the cardioid in the Mandelbrot set is warped to give the appearance of rotation.
The transformation is built up from smaller components, including:
- mapping of the cardioid to a circle
- Moebius transform of the circle to a straight line
- linear translation (which is animated)
- the inverses of the linear translation
- the inverse of Moebius transform of the circle to a straight line
These transformations and their derivatives (for distance estimator colouring) are described here: https://mathr.co.uk/blog/2013-12-16_stretching_cusps.html
The program to render the animation was implemented in C using the mandelbrot-graphics library found here: https://code.mathr.co.uk/mandelbrot-graphics The program is found in the repository as c/bin/m-cardioid/warping.c https://code.mathr.co.uk/mandelbrot-graphics/blob/60adc5ab8f14aab1be479469dfcf5ad3469feea0:/c/bin/m-cardioid-warping.c
What it the relation between x and internal angle ?
Hairness
m-stretching-cusps
One can add usage description :
if (! (argc == 7)) {
printf("no input \n");
printf("example usage : \n");
printf("%s re(nucleus) im(nucleus) period t_zero t_one t_infinity \n", argv[0] );
printf("%s 0 0 1 ? ? ? \n", argv[0] );
return 1;
}
What values should I put instead of ???
bond point c coordinates, corresponding to
- zero <- a/b
- one <- (a+c)/(b+d)
- infinity <- c/d
to have the cusp at c/d stretched out to infinity, with a/b in the center of the view (mapped to 0)
m-render
It is a base program for others.
This fragment of code describes how to use it :
int main(int argc, char **argv) {
if (argc != 8) {
fprintf(stderr, "usage: %s out.png width height creal cimag radius maxiters\n", argv[0]);
return 1;
}
example use will be :
m-render a.png 1000 1000 -0.75 0 1.5 10000
The result is Mandelbrot set boundary using DEM
m-streching-feigenbaum.c
Feigenbaum stretch with external rays ( period doubling cascade)
m-subwake-diagram-a
m-subwake-diagram-b
m-subwake-diagram-c
