Archivo:Wakes near the period 1 continent in the Mandelbrot set.png
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Tamaño de esta previsualización: 600 × 600 píxeles. Otras resoluciones: 240 × 240 píxeles | 480 × 480 píxeles | 768 × 768 píxeles | 1024 × 1024 píxeles | 2048 × 2048 píxeles | 4096 × 4096 píxeles.
Archivo original (4096 × 4096 píxeles; tamaño de archivo: 1,54 MB; tipo MIME: image/png)
Resumen
| Descripción |
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). |
| Fecha | |
| Fuente | Trabajo propio |
| Autor | Claude Heiland-Allen |
| Otras versiones |
  |
Resumen
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 :
- 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-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;
}
Licencia
Yo, el titular de los derechos de autor de esta obra, la publico en los términos de la siguiente licencia:
Este archivo está disponible bajo la licencia Creative Commons Attribution-Share Alike 4.0 International.
- Eres libre:
- de compartir – de copiar, distribuir y transmitir el trabajo
- de remezclar – de adaptar el trabajo
- Bajo las siguientes condiciones:
- atribución – Debes otorgar el crédito correspondiente, proporcionar un enlace a la licencia e indicar si realizaste algún cambio. Puedes hacerlo de cualquier manera razonable pero no de manera que sugiera que el licenciante te respalda a ti o al uso que hagas del trabajo.
- compartir igual – En caso de mezclar, transformar o modificar este trabajo, deberás distribuir el trabajo resultante bajo la misma licencia o una compatible como el original.
Historial del archivo
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| Fecha y hora | Miniatura | Dimensiones | Usuario | Comentario | |
|---|---|---|---|---|---|
| actual | 15:21 17 feb 2016 | | 4096 × 4096 (1,54 MB) | wikimediacommons>CM | User created page with UploadWizard |
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