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File:Wakes along the main antenna in the Mandelbrot set.png

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Summary

Description
English: Wakes along the main antenna in the Mandelbrot set. Boundary of the Mandelbrot set rendered with distance estimation (exterior and interior). Labelled with periods (blue), internal addresses (green) and external angles and rays (red).
Date
Source Own work
Author Claude Heiland-Allen

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  • 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-c.c

Dependencies :

C src code

/*
http://code.mathr.co.uk/mandelbrot-graphics/blob/HEAD:/c/bin/m-subwake-diagram-c.c
by Claude Heiland-Allen	

*/
#include <mandelbrot-graphics.h>
#include <mandelbrot-numerics.h>
#include <mandelbrot-symbolics.h>
#include <cairo.h>
#include <stdio.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 angle) {
  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_translate(cr, creal(c), cimag(c));
  cairo_rotate(cr, angle);
  cairo_translate(cr, - te.x_bearing - te.width / 2, - 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_external_ray(m_image *image, m_d_transform *transform, const char *angle, m_pixel_t colour, double pt, m_pixel_t lcolour, bool plabel, m_pixel_t acolour, const char *addr) {
  int maxiters = 1024;

  m_binangle btheta;
  m_binangle_init(&btheta);
  m_binangle_from_string(&btheta, angle);
  int period = btheta.per.length;

  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;
  double _Complex c1 = 0;
  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);
    c1 = c;
    double _Complex dc = 1;
    double t = cimag(c) > 0 ? twopi / 4 : -twopi / 4;
    m_d_transform_reverse(transform, &c, &dc);
    double h = fabs(cimag(c) - m_image_get_height(image) / 2);
    if (h > m_image_get_height(image) / 6) {
      continue;
    }
    if (first) {
      cairo_save(cr);
      cairo_translate(cr, creal(c), cimag(c));
      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, angle);
      cairo_fill(cr);
      cairo_restore(cr);
      cairo_move_to(cr, creal(c), cimag(c));
      first = false;
    } else {
      cairo_line_to(cr, creal(c), cimag(c));
    }
  }
  cairo_stroke(cr);
  cairo_destroy(cr);

  if (plabel) {
    double _Complex nucleus;
    m_d_nucleus(&nucleus, c1, period, 64);  
    char speriod[100];
    snprintf(speriod, 100, "%d", period);
    draw_label(image, transform, nucleus, speriod, pt, lcolour, 0);
    draw_label(image, transform, nucleus + 0.005 + I * 0.005, addr, pt / 2, acolour, -twopi / 12);
  }
}

int main(int argc, char **argv) {
  (void) argc;
  (void) argv;
  int w = 16384;
  int h = 1024;

  double _Complex c3, c4, c5, c6, c7, c8;
  m_d_nucleus(&c3, -2, 3, 64);
  m_d_nucleus(&c4, -2, 4, 64);
  m_d_nucleus(&c5, -2, 5, 64);
  m_d_nucleus(&c6, -2, 6, 64);
  m_d_nucleus(&c7, -2, 7, 64);
  m_d_nucleus(&c8, -1.4, 8, 64);

  double er = 600;
  int maxiters = 8192;
  const char *filename = "subwake-diagram-c.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 = 96;

  int retval = 1;
  m_image *image = m_image_new(w, h);
  if (image) {
    double _Complex c = (c7 + c8) / 2;
    double r = (2.03 + creal(c)) * h / (double) w;
    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);
        /*
        $ cat feature-database.csv | grep True | grep ^[1-7], | grep -v / | (
          IFS=,
          while read p i a n1 d1 n2 d2 rest
          do
            echo ", { \"`m-binangle-from-rational $n1/$d1`\", \"`m-binangle-from-rational $n2/$d2`\", \"$a\" }"
          done
        )
        */
        const char *angles[19][3] =
{ { ".(011)", ".(100)", "1 2 3" }
, { ".(0111)", ".(1000)", "1 2 3 4" }
, { ".(01111)", ".(10000)", "1 2 3 4 5" }
, { ".(01110)", ".(10001)", "1 2 3 5" }
, { ".(01101)", ".(10010)", "1 2 4 5" }
, { ".(011111)", ".(100000)", "1 2 3 4 5 6" }
, { ".(011110)", ".(100001)", "1 2 3 4 6" }
, { ".(011101)", ".(100010)", "1 2 3 5 6" }
, { ".(011010)", ".(100101)", "1 2 4 6" }
, { ".(0111111)", ".(1000000)", "1 2 3 4 5 6 7" }
, { ".(0111110)", ".(1000001)", "1 2 3 4 5 7" }
, { ".(0111101)", ".(1000010)", "1 2 3 4 6 7" }
, { ".(0111100)", ".(1000011)", "1 2 3 4 7" }
, { ".(0111011)", ".(1000100)", "1 2 3 5 6 7" }
, { ".(0111010)", ".(1000101)", "1 2 3 5 7" }
, { ".(0111001)", ".(1000110)", "1 2 3 6 7" }
, { ".(0110110)", ".(1001001)", "1 2 4 5 7" }
, { ".(0110101)", ".(1001010)", "1 2 4 6 7" }
, { ".(01101001)", ".(10010110)", "1 2 4 8" }
};
        for (int a = 0; a < 19; ++a) {
          for (int b = 0; b < 2; ++b) {
            draw_external_ray(image, transform, angles[a][b], red, pt, blue, b == 0, green, angles[a][2]);
          }
        }

        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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17 February 2016

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Date/TimeThumbnailDimensionsUserComment
current14:21, 17 February 2016Thumbnail for version as of 14:21, 17 February 201616,384 × 1,024 (3.07 MB)CMUser created page with UploadWizard

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