File:Wakes near the period 3 island in the Mandelbrot set.png
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Size of this preview: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels | 4,096 × 4,096 pixels.
Original file (4,096 × 4,096 pixels, file size: 1.57 MB, MIME type: image/png)
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This is a file from the Wikimedia Commons |
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 |
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 :
- http://code.mathr.co.uk/mandelbrot-graphics
- http://code.mathr.co.uk/mandelbrot-numerics
- http://code.mathr.co.uk/mandelbrot-symbolics
- https://cairographics.org/
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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