File:Julia set z+z^5.png
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Summary[edit]
DescriptionJulia set z+z^5.png |
English: Julia set for f(z) = z+z^5 |
Date | |
Source | Own work |
Author | Adam majewski |
Other versions |
C src code[edit]
This program creates 3 pgm files.
Convert one image to png using Image Magic :
convert 0.420000.pgm -resize 1000x1000 p1.png
/*
* c program:
* 1. draws Filled-in Julia setfor Fc(z)=z+z^5
* using :
* - boolean escape time ( exterior / interior)
* - attraction time and checking angle ( components of interior , see GiveColorOfInterior)
* -------------------------------
* 2. technic of creating ppm file is based on the code of Claudio Rocchini
* http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg
* create 24 bit color graphic file , portable pixmap file = PPM
* see http://en.wikipedia.org/wiki/Portable_pixmap
* to see the file use external application ( graphic viewer)
* ---------------------------------
* I think that creating graphic can't be simpler
*
* gcc z1.c -Wall -lm
*
* time ./a.out
*
* ============= const int iXmax = 1000; const int iYmax = 1000;
* TargetRadiusInPixels = iXmax/15.0;
*
* real 0m9.259s user 0m7.680s sys 0m0.060s
*
*/
#include <stdio.h>
#include <stdlib.h> // malloc
#include <math.h>
#include <string.h> // strcat
const int iXmax = 2000;
const int iYmax = 2000;
int iSize; //=iXmax * iYmax;
/* target set for points falling into alfa fixed point
* is a circle around alfa fixed point with radius = AR
*/
double AR;
//radius of target set around alfa fixed point in world coordinate AR = PixelWidth * TargetWidth;
double AR2;
//= AR * AR;
double TargetRadiusInPixels;
//radius of target set in pixels;
//memmory 1 D arrays
unsigned char *data;
unsigned char *edge;
int i;
//index of array
/*
* gives position of 2D point (iX,iY) in 1D array ; uses also global
* variable iWidth
*/
unsigned int
Give_i(unsigned int ix, unsigned int iy)
{
return ix + iy * iYmax;
}
//save data array to pgm file
int
SaveArray2PGMFile(unsigned char data[], double t)
{
FILE *fp;
const unsigned int MaxColorComponentValue = 255; /* color component is
* coded from 0 to 255 ;
* it is 8 bit color
* file */
char name [10]; /* name of file */
sprintf(name, "%f", t); /* */
char *filename = strcat(name, ".pgm");
char *comment = "# "; /* comment should start with # */
/* save image to the pgm file */
fp = fopen(filename, "wb"); /* create new file,give it a name and
* open it in binary mode */
fprintf(fp, "P5\n %s\n %u %u\n %u\n", comment, iXmax, iYmax, MaxColorComponentValue); /* write header to the
* file */
fwrite(data, iSize, 1, fp); /* write image data bytes to the file
* in one step */
printf("File %s saved. \n", filename);
fclose(fp);
return 0;
}
//all points of interior fall into fixed point z = 0
// check at what angle = which quadrant
unsigned char
GiveColorOfInterior(double x, double y)
{
if (x > 0.0 && y > 0.0)
return 235;
if (x > 0.0 && y < 0.0)
return 225;
if (x < 0.0 && y > 0.0)
return 215;
//if (x < 0 && y < 0)
return 185;
}
int
AddBoundaries(unsigned char data[])
{
unsigned int iX, iY; /* indices of 2D virtual array (image) =
* integer coordinate */
unsigned int i; /* index of 1D array */
/* sobel filter */
unsigned char G, Gh, Gv;
printf(" find boundaries in data array using Sobel filter\n");
for (iY = 1; iY < iYmax - 1; ++iY) {
for (iX = 1; iX < iXmax - 1; ++iX) {
Gv =
data[Give_i(iX - 1, iY + 1)] + 2 * data[Give_i(iX, iY + 1)] +
data[Give_i(iX - 1, iY + 1)] - data[Give_i(iX - 1, iY - 1)] -
2 * data[Give_i(iX - 1, iY)] - data[Give_i(iX + 1, iY - 1)];
Gh =
data[Give_i(iX + 1, iY + 1)] + 2 * data[Give_i(iX + 1, iY)] +
data[Give_i(iX - 1, iY - 1)] - data[Give_i(iX + 1, iY - 1)] -
2 * data[Give_i(iX - 1, iY)] - data[Give_i(iX - 1, iY - 1)];
G = sqrt(Gh * Gh + Gv * Gv);
i = Give_i(iX, iY); /* compute index of 1D array
* from indices of 2D array */
if (G == 0) {
edge[i] = 255;
}
/* background */
else {
edge[i] = 0;
} /* boundary */
}
}
printf("copy boundaries from edge array to data array \n");
for (iY = 1; iY < iYmax - 1; ++iY) {
for (iX = 1; iX < iXmax - 1; ++iX) {
i = Give_i(iX, iY);
if (edge[i] == 0)
data[i] = 0;
}
}
return 0;
}
int
main()
{
/* screen ( integer) coordinate */
int iX , iY;
iSize = iXmax * iYmax;
//
/* world ( double) coordinate = parameter plane */
const double xMin = -1.2;
const double xMax = 1.2;
const double yMin = -1.2;
const double yMax = 1.2;
/* */
double PixelWidth = (xMax - xMin) / iXmax;
double PixelHeight = (yMax - yMin) / iYmax;
//
/* color component ( R or G or B) is coded from 0 to 255 */
/* it is 24 bit color RGB file */
//const int MaxColorComponentValue = 255;
//FILE * fp;
//char *filename = "f2.pgm";
//char *comment = "# "; /* comment should start with # */
unsigned char color;
double x , y, tempx, /* Z=x+y*i */
x0 , y0, /* Z0 = x0 + y0*i */
x2 , y2; /* x2=x*x; y2=y*y */
double x2y2;
//, y4, x4, x2my2;
int Iteration;
const int IterationMax = 2000;
/* bail-out value , radius of circle ; */
double EscapeRadius = 2.0;
double ER2 = EscapeRadius * EscapeRadius;
TargetRadiusInPixels = iXmax / 15.0;
//= 15.0;
//radius of target set in pixels;
Maybe increase to 20 = 1000 / 50
AR = PixelWidth * TargetRadiusInPixels;
//!!!!important value(and precision and time of creation of the pgm image)
AR2 = AR * AR;
/* create dynamic 1D arrays for colors ( shades of gray ) */
data = malloc(iSize * sizeof(unsigned char));
edge = malloc(iSize * sizeof(unsigned char));
if (edge == NULL || edge == NULL) {
fprintf(stderr, " Could not allocate memory\n");
return 1;
} else
fprintf(stderr, " memory is OK \n");
/* compute and write image data bytes to the file */
for (iY = 0; iY < iYmax; ++iY) {
y0 = yMax - iY * PixelHeight; /* reverse Y axis */
if (fabs(y0) < PixelHeight / 2)
y0 = 0.0; /* */
printf(" iY = %d from %d\r", iY, iYmax);
//info
for (iX = 0; iX < iXmax; ++iX) { /* initial value of orbit Z0 */
x0 = xMin + iX * PixelWidth;
/* Z = Z0 */
x = x0;
y = y0;
x2 = x * x;
y2 = y * y;
x2y2 = x2 + y2;
//x2my2 = x2 * y2;
for (Iteration = 0; Iteration < IterationMax - 1; Iteration++) {
if ((x2y2) > ER2) {
color = 245;
break;
} /* exterior of Filled-in Julia set */
if ((x2y2) < AR2) {
color = GiveColorOfInterior(x, y);
break;
} /* interior of Filled-in Julia set */
//z + z ^ 5
tempx = 5.0 * x * y * y * y * y - 10.0 * x * x * x * y * y + x * x * x * x * x + x;
//5 * x * y ^ 4 - 10 * x ^ 3 * y ^ 2 + x ^ 5 + x
y = y * y * y * y * y - 10.0 * x * x * y * y * y + 5.0 * x * x * x * x * y + y;
//y ^ 5 - 10 * x ^ 2 * y ^ 3 + 5 * x ^ 4 * y + y
x = tempx;
//
x2 = x * x;
y2 = y * y;
//y4 = y2 * y2;
//x4 = x2 * x2;
x2y2 = x2 + y2;
//x2my2 = x2 * y2;
};
//if (Iteration == IterationMax) {
printf(" Iteration==IterationMax\r");
color = GiveColorOfInterior(x, y);
}
i = Give_i(iX, iY);
data[i] = color;
}
}
SaveArray2PGMFile(data, 0.22);
AddBoundaries(data);
SaveArray2PGMFile(edge, 0.32);
SaveArray2PGMFile(data, 0.42);
free(data);
free(edge);
return 0;
}
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported 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.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
You may select the license of your choice.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:42, 24 February 2013 | 1,000 × 1,000 (61 KB) | Soul windsurfer (talk | contribs) | better quality | |
21:12, 18 January 2013 | 2,000 × 2,000 (26 KB) | Soul windsurfer (talk | contribs) | {{Information |Description ={{en|1=Julia set for f(z) = z+z^5}} |Source ={{own}} |Author =Adam majewski |Date =2013-01-18 |Permission = |other_versions = }} |
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