m-perturbator is the fractal software: Mandelbrot set explorer GUI by Claude Heiland-Allen with:

annotation
efficient deep zooming ( perturbation)

Versions

mandelbrot-book GUI porgram - old version
m-perturbator-colourize
m-perturbator-glfw3
m-perturbator-gtk ( annotations)

Install

see README.md from repo

From parent dir :

 make -C mandelbrot-perturbator/c/lib install
 make -C mandelbrot-perturbator/c/bin install

dependecies

mandelbrot symbolics
mandelbrot numerics
GTK
GLEW
GLFW

 apt-get install libsndfile-dev
 sudo apt-get install build-essential libgtk-3-dev
 sudo apt-get install libglfw3-dev
 sudo apt-get install libglew-dev

Installs into ~/opt by default, you can change that with make options (e.g. `make -C c/lib install prefix=~/fantastic-software/`).

sudo apt install git build-essential libpari-dev libmpc-dev libgtk-3-dev libsndfile-dev libglfw3-dev libglew-dev
mkdir -p ~/opt/src
cd ~/opt/src/
git clone https://code.mathr.co.uk/mandelbrot-symbolics.git
git clone https://code.mathr.co.uk/mandelbrot-numerics.git
git clone https://code.mathr.co.uk/mandelbrot-perturbator.git
cd ~/opt/src/mandelbrot-symbolics
make -C c/lib/ install
make -C c/bin/ install
cd ~/opt/src/mandelbrot-numerics
make -C c/lib/ install
make -C c/bin/ install
cd ~/opt/src/mandelbrot-perturbator
make -C c/lib/ install
make -C c/bin/ install
cd
LD_LIBRARY_PATH=~/opt/lib ~/opt/bin/m-perturbator-gtk

update

 git pull

Run

m-perturbator-gtk
m-perturbator-glfw3
m-perturbator-offline
m-perturbator-automorph

Example:

 export LD_LIBRARY_PATH=${HOME}/opt/lib
 export PATH=${HOME}/opt/bin:${PATH}
 ./m-perturbator-gtk

atom

N

N*2 and N/2 change the iteration count limit of the image (you may need to increase it when zooming deeper)

Filaments

Filaments traces rays to prune filaments from minibrots and embedded Julia sets. See https://mathr.co.uk/blog/2013-10-02_islands_in_the_hairs.html and https://post.lurk.org/@mathr/102922605930156945 (the embedded Julia set rays are found by prepending the periodic block of the central island rays to periodic blocks of the influencing island rays)

Mu-unit

definition from Mu-Ency by R Munafo^[1]

Steps:

select nucleus
first click on the menu
then using mouse left click and hold make a circle over a space where nucleus is. Number showing period of the nucleus is shown on the image and on the Annotations panel on the right
mark the nucleus number on the Annotations panel and click Mu-Unit menu item

Nucleus

Nucleus of a Mu-Atom^[2] = center of hyperbolic component of the Mandelbrot set

Steps:

select nucleus
first click on the menu
then using mouse left click and hold make a circle over a space where nucleus is. Number showing period of the nucleus is shown on the image and on the Annotations panel on the right

Ray in

Draw parameter ray from infinity toward Mandelbrot set boundary

Options

external angle ( binary fraction),
preperiod ( positive int )
period ( positive int )
depth ( positive int)

Example of acceptable values of external angle ( without zero from the the whole-number^[3]) :

periodic : .(1)
preperiodic: .01(0110)
? .1(0)

Bad (non acceptable) values are

.1

One can chack it also in the web interface

case task_ray_in:
    {
      struct annotation *a = calloc(1, sizeof(*a));
      a->style = t->style;
      a->label = m_binangle_to_new_string(&t->u.ray_in.angle);
      a->tag = annotation_ray_in;
      m_binangle_init(&a->u.ray_in.angle);
      m_binangle_set(&a->u.ray_in.angle, &t->u.ray_in.angle);
      int depth = t->u.ray_in.depth;
      int sharpness = 16;
      mpq_t q;
      mpq_init(q);
      m_binangle_to_rational(q, &t->u.ray_in.angle);
      mpq_canonicalize(q);
      m_r_exray_in *ray = m_r_exray_in_new(q, sharpness);
      mpq_clear(q);
      int i = 0;
      double total = 0.5 * sharpness * depth * (1 + depth);
      double progress = 0;
      int increment = 1;
      m_newton success = m_failed;
      int first = 1;
      while (! t->cancelled && (m_failed != (success = m_r_exray_in_step(ray, 64))))
      {
        progress = progress + increment;
        t->progress = progress / total;
        task_set_progress(t);
        a->u.ray_in.line_start = point_new(a->u.ray_in.line_start);
        m_r_exray_in_get(ray, a->u.ray_in.line_start->xy);
        if (first)
        {
          first = 0;
          a->u.ray_in.line_end = a->u.ray_in.line_start;
        }
        if (++i >= sharpness)
        {
          i = 0;
          increment = increment + 1;
          if (increment >= depth)
          {
            success = m_converged;
            break;
          }
        }
        if (success == m_converged)
        {
          break;
        }
      }
      a->u.ray_in.ray = ray;
      a->u.ray_in.depth = increment;
      if (! t->cancelled && success == m_converged)
      {
        g_async_queue_push(t->output, a);
      }
      else
      {
        free_annotation(a);
      }
      break;
    } // task_ray_in

Ray out

Collecting bits when tracing outwards

 case task_ray_out:
    {
      struct annotation *a = calloc(1, sizeof(*a));
      a->tag = annotation_ray_out;
      a->style = t->style;
      char *accumulated_bits = malloc(t->u.ray_out.dwell + 10);
      int i = 0;
      int sharpness = 16;
      m_r_exray_out *ray = m_r_exray_out_new(t->u.ray_out.c, sharpness, t->u.ray_out.dwell * 2, 65536);
      double total = 0.5 * sharpness * t->u.ray_out.dwell * (1 + t->u.ray_out.dwell);
      double progress = 0;
      double increment = t->u.ray_out.dwell;
      m_newton success = m_failed;
      int first = 1;
      while (! t->cancelled && (m_failed != (success = m_r_exray_out_step(ray))))
      {
        progress = progress + increment;
        t->progress = progress / total;
        task_set_progress(t);
        a->u.ray_out.line_start = point_new(a->u.ray_out.line_start);
        if (first)
        {
          first = 0;
          a->u.ray_out.line_end = a->u.ray_out.line_start;
        }
        m_r_exray_out_get(ray, a->u.ray_out.line_start->xy);
        if (m_r_exray_out_have_bit(ray))
        {
          increment = increment - 1;
          bool bit = m_r_exray_out_get_bit(ray);
          accumulated_bits[i++] = bit ? '1' : '0';
          if (i >= t->u.ray_out.dwell + 10 - 1)
          {
            // should never happen?
            success = m_failed;
            break;
          }
        }
        if (success == m_converged)
        {
          break;
        }
      }
      if (! t->cancelled && success == m_converged)
      {
        accumulated_bits[i] = 0;
        int nbits = i;
        char *reversed_bits = malloc(nbits + 1);
        for (int i = 0; i < nbits; ++i)
        {
          reversed_bits[i] = accumulated_bits[nbits-1 - i];
        }
        reversed_bits[nbits] = 0;
        a->label = reversed_bits;
        g_async_queue_push(t->output, a);
      }
      else
      {
        free_annotation(a);
      }
      free(accumulated_bits);
      m_r_exray_out_delete(ray);
      break;
    } // task_ray_out

ray extended

 case task_ray_extend:
    {
      struct annotation *a = t->u.ray_extend.anno;
      a->style = t->style;
      m_r_exray_in *ray = a->u.ray_in.ray;
      int sharpness = 16; // FIXME must match ray_in above
      int start_depth = a->u.ray_in.depth;
      int end_depth = t->u.ray_extend.depth;
      int i = 0;
      double total = 0.5 * sharpness * (end_depth - start_depth) * (end_depth + start_depth);
      double progress = 0;
      int increment = start_depth;
      m_newton success = m_failed;
      while (! t->cancelled && (m_failed != (success = m_r_exray_in_step(ray, 64))))
      {
        progress = progress + increment;
        t->progress = progress / total;
        task_set_progress(t);
        a->u.ray_in.line_start = point_new(a->u.ray_in.line_start);
        m_r_exray_in_get(ray, a->u.ray_in.line_start->xy);
        if (++i >= sharpness)
        {
          i = 0;
          increment = increment + 1;
          if (increment >= end_depth)
          {
            success = m_converged;
            break;
          }
        }
        if (success == m_converged)
        {
          break;
        }
      }
      a->u.ray_in.depth = increment;
      g_async_queue_push(t->output, a);
      break;
    } // task_ray_extend

wake

to highlight a wake you need two rays (must both be Ray In) with equal (pre)periods landing at the same point (or close enough in screen-space). select one of them, then chose the wake left/right depending if the other ray is anticlockwise or clockwise from the selected ray.

Files

mp extension is used by mandelbrot-perturbator for the parameter files

program = "m-perturbator-gtk"
version ="v0.2-8-g471fa29"
width = 1705
height = 1128
theme = "light"
colour = "low"
key = "none"
view.default = { precision = 9367, re = 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radius = "9.1837241657335749e-2805", iterations = 4194304 }
annotations = [
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]

Doc

fractalforums post : m-perturbator-gtk demo-screencasts
a small user manual
Perturbator uses GTK for GUI, implemented in C. Pro: native language of GTK is C so documentation applies directly; C inner loops are fast. Con: manual memory management is a pain.
video on diode : Parallel Evolution with m-perturbator-gtk

Problems

run

 m-perturbator-glfw3

result :

 m-perturbator-glfw3: command not found

solution :

 ~/mandelbrot-perturbator/c/bin/m-perturbator-glfw3

error while loading shared libraries: libmandelbrot-perturbator.so: cannot open shared object file: No such file or directory

Check ldconfig path:^[4]

 ldconfig -p>l.txt

If there is no libmandelbrot-perturbator.so library file in that path, find where the library file is placed if you don't know it:

 sudo find / -name libmandelbrot-perturbator.so

The result :

 /home/a/opt/lib/libmandelbrot-perturbator.so

Check for the existence of the dynamic library path environment variable(LD_LIBRARY_PATH):^[5]

 echo $LD_LIBRARY_PATH

So the solution :

 export LD_LIBRARY_PATH=${HOME}/opt/lib

References

[1] Mu-unit from the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018.

[2] Nucleus From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018

[3] ting_constant in cpp ref

[4] stackoverflow question: error-while-loading-shared-libraries-cannot-open-shared-object-file-no-such-fi

[5] stackoverflow question: linux-error-while-loading-shared-libraries-cannot-open-shared-object-file-no-s

[1]

[2]

[3]

[4]

[5]

Fractals/mandelbrot-perturbator

Contents