File:Wakes near the period 3 island in the Mandelbrot set.png

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Summary

Description	English: Wakes near the period 3 island in the Mandelbrot set. Boundary of the Mandelbrot set rendered with distance estimation (exterior and interior). Labelled with periods (blue), internal angles and rays (green) and external angles and rays (red).
Date	17 February 2016
Source	Own work
Author	Claude Heiland-Allen

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Summary

This image is made with c code, see : http://code.mathr.co.uk/mandelbrot-graphics/blob/HEAD:/c/bin/m-subwake-diagram-b.c

Dependencies :

C src code

/*
http://code.mathr.co.uk/mandelbrot-graphics/blob/HEAD:/c/bin/m-subwake-diagram-b.c
by 
*/Claude Heiland-Allen
#include <mandelbrot-graphics.h>
#include <mandelbrot-numerics.h>
#include <mandelbrot-symbolics.h>
#include <cairo.h>

const double twopi = 6.283185307179586;

void draw_label(m_image *image, m_d_transform *transform, double _Complex c0, const char *text, double pt, m_pixel_t colour) {
  double _Complex c = c0;
  double _Complex dc = 1;
  m_d_transform_reverse(transform, &c, &dc);
  cairo_surface_t *surface = m_image_surface(image);
  cairo_t *cr = cairo_create(surface);
  cairo_select_font_face(cr, "LMSans10", CAIRO_FONT_SLANT_NORMAL, CAIRO_FONT_WEIGHT_NORMAL);
  cairo_set_font_size(cr, pt);
  cairo_text_extents_t te;
  cairo_text_extents(cr, text, &te);
  cairo_move_to(cr, creal(c) - te.x_bearing - te.width / 2, cimag(c) - te.y_bearing - te.height / 2);
  cairo_text_path(cr, text);
  cairo_set_source_rgba(cr, m_pixel_red(colour), m_pixel_green(colour), m_pixel_blue(colour), m_pixel_alpha(colour));
  cairo_fill(cr);
  cairo_destroy(cr);
}

void draw_internal_ray(m_image *image, m_d_transform *transform, int period, double _Complex nucleus, const char *angle, double pt, m_pixel_t colour) {
  int steps = 128;
  mpq_t theta;
  mpq_init(theta);
  mpq_set_str(theta, angle, 10);
  mpq_canonicalize(theta);
  double a = twopi * mpq_get_d(theta);
  mpq_clear(theta);
  double _Complex interior = cos(a) + I * sin(a);

  double _Complex cl = 0, cl2 = 0;
  double _Complex c = nucleus;
  double _Complex z = c;
  cairo_surface_t *surface = m_image_surface(image);
  cairo_t *cr = cairo_create(surface);
  cairo_set_source_rgba(cr, m_pixel_red(colour), m_pixel_green(colour), m_pixel_blue(colour), m_pixel_alpha(colour));
  for (int i = 0; i < steps; ++i) {
    if (2 * i == steps) {
      cl = c;
    }
    if (2 * i == steps + 2) {
      cl2 = c;
    }
    double radius = (i + 0.5) / steps;
    m_d_interior(&z, &c, z, c, radius * interior, period, 64);
    double _Complex pc = c;
    double _Complex pdc = 1;
    m_d_transform_reverse(transform, &pc, &pdc);
    if (i == 0) {
      cairo_move_to(cr, creal(pc), cimag(pc));
    } else {
      cairo_line_to(cr, creal(pc), cimag(pc));
    }
  }
  cairo_stroke(cr);
  if (a != 0) {
    double t = carg(cl2 - cl);
    cairo_save(cr);
    double _Complex dcl = 1;
    m_d_transform_reverse(transform, &cl, &dcl);
    cairo_translate(cr, creal(cl), cimag(cl));
    cairo_rotate(cr, -t);
    cairo_translate(cr, 0, -pt/3);
    cairo_select_font_face(cr, "LMSans10", CAIRO_FONT_SLANT_NORMAL, CAIRO_FONT_WEIGHT_NORMAL);
    cairo_set_font_size(cr, pt);
    cairo_text_path(cr, angle);
    cairo_fill(cr);
    cairo_restore(cr);
  }
  cairo_destroy(cr);
}

void draw_external_ray(m_image *image, m_d_transform *transform, const char *angle, m_pixel_t colour, double dx, double dy, double _Complex c0, double r0) {
  int maxiters = 1024;

  m_block blo, bhi;
  m_block_init(&blo);
  m_block_init(&bhi);
  m_block_from_string(&blo, "011");
  m_block_from_string(&bhi, "100");
  m_binangle btheta0;
  m_binangle_init(&btheta0);
  m_binangle_from_string(&btheta0, angle);
  m_binangle btheta;
  m_binangle_init(&btheta);
  m_binangle_tune(&btheta, &btheta0, &blo, &bhi);
  m_binangle_clear(&btheta0);
  m_block_clear(&blo);
  m_block_clear(&bhi);
  char angle2[m_binangle_strlen(&btheta) + 1];
  m_binangle_to_string(angle2, &btheta);

  mpq_t qtheta;
  mpq_init(qtheta);
  m_binangle_to_rational(qtheta, &btheta);
  m_binangle_clear(&btheta);
  m_d_exray_in *ray = m_d_exray_in_new(qtheta, 8);
  mpq_clear(qtheta);

  cairo_surface_t *surface = m_image_surface(image);
  cairo_t *cr = cairo_create(surface);
  cairo_set_source_rgba(cr, m_pixel_red(colour), m_pixel_green(colour), m_pixel_blue(colour), m_pixel_alpha(colour));
  bool first = true;
  for (int i = 0; i < maxiters; ++i) {
    if (m_failed == m_d_exray_in_step(ray, 64)) {
      break;
    }
    double _Complex c = m_d_exray_in_get(ray);
    if (cabs(c - c0) > r0) {
      continue;
    }
    double t = carg(c - c0);
    double _Complex dc = 1;
    m_d_transform_reverse(transform, &c, &dc);
    if (first) {
      cairo_save(cr);
      cairo_translate(cr, creal(c) + dx, cimag(c) + dy);
      cairo_rotate(cr, -t);
      cairo_select_font_face(cr, "LMMono10", CAIRO_FONT_SLANT_NORMAL, CAIRO_FONT_WEIGHT_NORMAL);
      cairo_set_font_size(cr, 48);
      cairo_text_path(cr, angle2);
      cairo_fill(cr);
      cairo_restore(cr);
      cairo_move_to(cr, creal(c) + dx, cimag(c) + dy);
      first = false;
    } else {
      cairo_line_to(cr, creal(c), cimag(c));
    }
  }
  cairo_stroke(cr);
  cairo_destroy(cr);
}

int main(int argc, char **argv) {
  (void) argc;
  (void) argv;
  int w = 4096;
  int h = 4096;

  int p = 3;
  double _Complex c1, c2, c3, c4a, c4b, c5, c3c2, c2c3;
  m_d_nucleus(&c1, -2, p * 1, 64);
  double size = cabs(m_d_size(c1, p * 1));
  m_d_nucleus(&c2, c1 - size, p * 2, 64);
  m_d_nucleus(&c3, c1 + I * size, p * 3, 64);
  m_d_nucleus(&c4a, c1 + size * 0.25 + size * 0.5 * I, p * 4, 64);
  m_d_nucleus(&c4b, c1 + size * 0.25 - size * 0.5 * I, p * 4, 64);
  m_d_nucleus(&c5,  c1 + size * 0.3 + size * 0.3 * I, p * 5, 64);
  m_d_nucleus(&c3c2, c3 + size * I * 0.1, p * 6, 64);
  m_d_nucleus(&c2c3, c2 - size * 0.25 + size * 0.25 * I, p * 6, 64);

  complex double c = (c1 + 3 * c2) / 4;
  double r = 3 * size;
  double r0 = sqrt(2) * size;
  double er = 600;
  int maxiters = 8192;
  const char *filename = "subwake-diagram-b.png";

  m_pixel_t red   = m_pixel_rgba(1, 0, 0, 1);
  m_pixel_t green = m_pixel_rgba(0, 0.5, 0, 1);
  m_pixel_t blue  = m_pixel_rgba(0, 0, 1, 1);
  m_pixel_t black = m_pixel_rgba(0, 0, 0, 1);
  m_pixel_t white = m_pixel_rgba(1, 1, 1, 1);
  double pt = 48 * 1.75 / 3;

  int retval = 1;
  m_image *image = m_image_new(w, h);
  if (image) {
    m_d_transform *transform = m_d_transform_rectangular(w, h, c, r);
    if (transform) {
      m_d_colour_t *colour = m_d_colour_minimal(white, black, white);
      if (colour) {
        m_d_render_scanline(image, transform, er, maxiters, colour);
        
        draw_internal_ray(image, transform, p * 1, c1, "1/2", pt, green);
        draw_internal_ray(image, transform, p * 1, c1, "1/3", pt, green);
        draw_internal_ray(image, transform, p * 1, c1, "1/4", pt, green);
        draw_internal_ray(image, transform, p * 1, c1, "1/5", pt, green);
        draw_internal_ray(image, transform, p * 1, c1, "3/4", pt, green);
        draw_internal_ray(image, transform, p * 2, c2, "0/1", pt, green);
        draw_internal_ray(image, transform, p * 2, c2, "1/3", pt, green);
        draw_internal_ray(image, transform, p * 3, c3, "0/1", 0.7 * pt, green);
        draw_internal_ray(image, transform, p * 3, c3, "1/2", 0.7 * pt, green);
        draw_internal_ray(image, transform, p * 3, c3, "1/3", 0.7 * pt, green);
        draw_internal_ray(image, transform, p * 3, c3, "1/4", 0.7 * pt, green);
        draw_internal_ray(image, transform, p * 3, c3, "3/4", 0.7 * pt, green);

        draw_external_ray(image, transform, ".(0)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(1)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(10)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(001)", red, 32, 32 - 32, c, r0);
        draw_external_ray(image, transform, ".(010)", red, -48 - 16, -32, c, r0);
        draw_external_ray(image, transform, ".(011)", red, 0, 16, c, r0);
        draw_external_ray(image, transform, ".(100)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(0001)", red, 0, -16, c, r0);
        draw_external_ray(image, transform, ".(0010)", red, 48, 48 - 32, c, r0);
        draw_external_ray(image, transform, ".(1101)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(1110)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(00001)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(00010)", red, 32, 32, c, r0);
        draw_external_ray(image, transform, ".(001010)", red, -64, -64 - 32, c, r0);
        draw_external_ray(image, transform, ".(010001)", red, 48, -32, c, r0);
        draw_external_ray(image, transform, ".(010110)", red, 0, 0, c, r0);
        draw_external_ray(image, transform, ".(011001)", red, 0, -16, c, r0);
        draw_external_ray(image, transform, ".(001001010)", red, -64, -64 - 32, c, r0);
        draw_external_ray(image, transform, ".(001010001)", red, -32, -32 - 32, c, r0);
        draw_external_ray(image, transform, ".(001001001010)", red, 0, 0 - 32, c, r0);
        draw_external_ray(image, transform, ".(001001010001)", red, -32, -32 - 32, c, r0);
        draw_external_ray(image, transform, ".(010010001010)", red, 48 - 16, -32, c, r0);
        draw_external_ray(image, transform, ".(010010010001)", red, 0 - 16, -32, c, r0);

        draw_label(image, transform, c1,   "3", 6 * pt, blue);
        draw_label(image, transform, c2,   "6", 3 * pt, blue);
        draw_label(image, transform, c3,   "9", 2 * pt, blue);
        draw_label(image, transform, c4a,  "12", 1.5 * pt, blue);
        draw_label(image, transform, c4b,  "12", 1.5 * pt, blue);
        draw_label(image, transform, c5,   "15", pt, blue);
        draw_label(image, transform, c2c3, "18", pt, blue);
        draw_label(image, transform, c3c2, "18", pt, blue);

        m_image_save_png(image, filename);
        retval = 0;
        m_d_colour_delete(colour);
      }
      m_d_transform_delete(transform);
    }
    m_image_delete(image);
  }
  return retval;
}

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	14:21, 17 February 2016		4,096 × 4,096 (1.57 MB)	CM	User created page with UploadWizard

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- External ray

File:Wakes near the period 3 island in the Mandelbrot set.png

Contents

Summary

Licensing

Summary

C src code

Captions

Items portrayed in this file

depicts

creator

some value

copyright status

copyrighted

copyright license

Creative Commons Attribution-ShareAlike 4.0 International

inception

17 February 2016

source of file

original creation by uploader

File history

File usage

Global file usage