Berkas:Wakes near the period 1 continent in the Mandelbrot set.png

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Ringkasan

Deskripsi
English: Wakes near the period 1 continent 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).
Tanggal
Sumber Karya sendiri
Pembuat Claude Heiland-Allen
Versi lainnya
Wakes along the main antenna in the Mandelbrot set
Wakes near the period 3 island in the Mandelbrot set

Ringkasan

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

Dependencies :

C src code

/*
http://code.mathr.co.uk/mandelbrot-graphics/blob/HEAD:/c/bin/m-subwake-diagram-a.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) {
  int maxiters = 1024;
  double r = sqrt(2);

  m_binangle btheta;
  m_binangle_init(&btheta);
  m_binangle_from_string(&btheta, angle);
  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 + 0.75) > r) {
      continue;
    }
    double t = carg(c + 0.75);
    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, angle);
      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;
  complex double c = -0.75;
  double r = 1.75;
  double er = 600;
  int maxiters = 8192;
  const char *filename = "subwake-diagram-a.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);

  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);

        double _Complex c3, c4a, c4b, c5, c3c2, c2c3;
        m_d_nucleus(&c3, 0 + I * 1, 3, 64);
        m_d_nucleus(&c4a, 0.25 + 0.5 * I, 4, 64);
        m_d_nucleus(&c4b, 0.25 - 0.5 * I, 4, 64);
        m_d_nucleus(&c5,  0.3 + 0.3 * I, 5, 64);
        m_d_nucleus(&c3c2, c3 + I * 0.1, 6, 64);
        m_d_nucleus(&c2c3, -1 - 0.25 + 0.25 * I, 6, 64);

        double pt = 48;
        
        draw_internal_ray(image, transform, 1, 0, "1/2", pt, green);
        draw_internal_ray(image, transform, 1, 0, "1/3", pt, green);
        draw_internal_ray(image, transform, 1, 0, "1/4", pt, green);
        draw_internal_ray(image, transform, 1, 0, "1/5", pt, green);
        draw_internal_ray(image, transform, 1, 0, "3/4", pt, green);
        draw_internal_ray(image, transform, 2, -1, "0/1", pt, green);
        draw_internal_ray(image, transform, 2, -1, "1/3", pt, green);
        draw_internal_ray(image, transform, 3, c3, "0/1", 0.7 * pt, green);
        draw_internal_ray(image, transform, 3, c3, "1/2", 0.7 * pt, green);
        draw_internal_ray(image, transform, 3, c3, "1/3", 0.7 * pt, green);
        draw_internal_ray(image, transform, 3, c3, "1/4", 0.7 * pt, green);
        draw_internal_ray(image, transform, 3, c3, "3/4", 0.7 * pt, green);

        draw_external_ray(image, transform, ".(01)", red, 0, 0);
        draw_external_ray(image, transform, ".(10)", red, 0, 0);
        draw_external_ray(image, transform, ".(001)", red, 32, 32);
        draw_external_ray(image, transform, ".(010)", red, -48, 0);
        draw_external_ray(image, transform, ".(011)", red, 0, 0);
        draw_external_ray(image, transform, ".(100)", red, 0, 0);
        draw_external_ray(image, transform, ".(0001)", red, 0, -16);
        draw_external_ray(image, transform, ".(0010)", red, 16, 16);
        draw_external_ray(image, transform, ".(1101)", red, 0, 0);
        draw_external_ray(image, transform, ".(1110)", red, 0, 0);
        draw_external_ray(image, transform, ".(00001)", red, 0, 0);
        draw_external_ray(image, transform, ".(00010)", red, 0, 16);
        draw_external_ray(image, transform, ".(001010)", red, -32, -32);
        draw_external_ray(image, transform, ".(010001)", red, 0, 0);
        draw_external_ray(image, transform, ".(010110)", red, 0, 0);
        draw_external_ray(image, transform, ".(011001)", red, 0, 0);
        draw_external_ray(image, transform, ".(001001010)", red, -48, -48);
        draw_external_ray(image, transform, ".(001010001)", red, 0, 0);
        draw_external_ray(image, transform, ".(001001001010)", red, 0, 0);
        draw_external_ray(image, transform, ".(001001010001)", red, -16, -16);
        draw_external_ray(image, transform, ".(010010001010)", red, 32, 0);
        draw_external_ray(image, transform, ".(010010010001)", red, 0, 0);

        draw_label(image, transform,  0,   "1", 6 * pt, blue);
        draw_label(image, transform, -1,   "2", 3 * pt, blue);
        draw_label(image, transform, c3,   "3", 2 * pt, blue);
        draw_label(image, transform, c4a,  "4", 1.5 * pt, blue);
        draw_label(image, transform, c4b,  "4", 1.5 * pt, blue);
        draw_label(image, transform, c5,   "5", pt, blue);
        draw_label(image, transform, c2c3, "6", pt, blue);
        draw_label(image, transform, c3c2, "6", 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;
}

Lisensi

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atribusi berbagi serupa
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Berdasarkan ketentuan berikut:
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  • berbagi serupa – Apabila Anda menggubah, mengubah, atau membuat turunan dari materi ini, Anda harus menyebarluaskan kontribusi Anda di bawah lisensi yang sama seperti lisensi pada materi asli.

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17 Februari 2016

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