File:Julia set z+z^5.png
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Summary
| Description |
English: Julia set for f(z) = z+z^5 |
| Date | |
| Source | Own work |
| Author | Adam majewski |
| Other versions |
C src code
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
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- to share – to copy, distribute and transmit the work
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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. |
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:42, 24 February 2013 | | 1,000 × 1,000 (61 KB) | Soul windsurfer | better quality |
| 21:12, 18 January 2013 |  | 2,000 × 2,000 (26 KB) | Soul windsurfer | {{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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