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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
Source Own work
Author Claude Heiland-Allen

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w:en:Creative Commons
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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;
}

Captions

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).

Items portrayed in this file

depicts

17 February 2016

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Date/TimeThumbnailDimensionsUserComment
current14:21, 17 February 2016Thumbnail for version as of 14:21, 17 February 20164,096 × 4,096 (1.57 MB)CMUser created page with UploadWizard

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