Fractals/mandelbrot-perturbator

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

  • annotation
  • efficient deep zooming ( perturbation)

Versions[edit | edit source]

Install[edit | edit source]

  • see README.md from repo

From parent dir : 

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

dependecies[edit | edit source]

  • 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[edit | edit source]

 git pull

Run[edit | edit source]

  • 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

Menu[edit | edit source]

atom[edit | edit source]

N[edit | edit source]

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

Filaments[edit | edit source]

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[edit | edit source]

  • 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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

 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[edit | edit source]

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[edit | edit source]

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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im = 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radius = "9.1837241657335749e-2805", iterations = 4194304 }
annotations = [
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]


Doc[edit | edit source]

Problems[edit | edit source]

run[edit | edit source]

 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[edit | edit source]

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[edit | edit source]

  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. ↑ floating_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
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