File:Mandelbrot set - Normal mapping.png
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Summary
DescriptionMandelbrot set - Normal mapping.png |
English: Mandelbrot set - Normal mapping |
Date | |
Source | Made using description ( algorithm ) by Arnaud Cheritat and with help of Claude Heiland-Allen |
Author | Adam majewski |
Other versions |
|
C source code
/*
c program: console, 1-file
normal.c
normal = Normal map effect Mandelbrot set
https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set
thx for help:
* Claude Heiland-Allen http://mathr.co.uk/blog/
--------------------------------
1. draws Mandelbrot set for Fc(z)=z*z +c
using Mandelbrot algorithm ( boolean escape time )
-------------------------------
2. technique 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)
-----
it is example for :
https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set
-------------
compile :
gcc normal.c -lm -Wall
./a.out
*/
#include < stdio.h >
#include < math.h >
#include < complex.h >
#define M_PI 3.14159265358979323846 /* pi */
/* screen ( integer) coordinate */
int iX, iY;
const int iXmax = 10000;
const int iYmax = 10001; // for main antenna
/* world ( double) coordinate = parameter plane*/
double Cx, Cy;
const double CxMin = -2.2;
const double CxMax = 0.8;
const double CyMin = -1.5;
const double CyMax = 1.5;
/* */
double PixelWidth; //=(CxMax-CxMin)/iXmax;
double PixelHeight; // =(CyMax-CyMin)/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 = "n10000.ppm"; // https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/File:M-bump-1.png
char * comment = "# "; /* comment should start with # */
static unsigned char color[3]; // 24-bit rgb color
/* */
const int IterationMax = 2000; // N in wiki
/* bail-out value for the bailout test for escaping points
radius of circle centered ad the origin, exterior of such circle is a target set */
const double EscapeRadius = 1000; // big !!!!
double complex give_c(int iX, int iY) {
double Cx, Cy;
Cy = CyMax - iY * PixelHeight;
Cx = CxMin + iX * PixelWidth;
return Cx + Cy * I;
}
/*
The dot product of two vectors a = [a1, a2, ..., an] and b = [b1, b2, ..., bn] is defined as:[1]
d = a1b1 + a2b2
*/
double cdot(double complex a, double complex b) {
return creal(a) * creal(b) + cimag(a) * cimag(b);
}
//
// output
//
double GiveReflection(double complex C, int iMax) {
int i = 0; // iteration
double complex Z = 0.0; // initial value for iteration Z0
double complex dC = 0.0; // derivative with respect to c
double reflection = FP_ZERO; // inside
double h2 = 1.5; // height factor of the incoming light
double angle = 45.0 / 360.0; // incoming direction of light in turns
double complex v = cexp(2.0 * angle * M_PI * I); // = exp(1j*angle*2*pi/360) // unit 2D vector in this direction
// incoming light 3D vector = (v.re,v.im,h2)
double complex u;
for (i = 0; i < iMax; i++) {
dC = 2.0 * dC * Z + 1.0;
Z = Z * Z + C;
if (cabs(Z) > EscapeRadius) { // exterior of M set
u = Z / dC;
u = u / cabs(u);
reflection = cdot(u, v) + h2;
reflection = reflection / (1.0 + h2); // rescale so that t does not get bigger than 1
if (reflection < 0.0) reflection = 0.0;
break;
}
}
return reflection;
}
int compute_color(complex double c, unsigned char color[3]) {
double reflection;
unsigned char b;
// compute
reflection = GiveReflection(c, IterationMax);
if (reflection == FP_ZERO) { /* interior of Mandelbrot set = inside_color = blue */
color[0] = 0; // M_waves
color[1] = 0;
color[2] = 127;
} else // exterior of Mandelbrot set = normal
{
b = 255 * reflection;
//b = (unsigned char) (255 - 255*potential );
color[0] = b; /* Red*/
color[1] = b; /* Green */
color[2] = b; /* Blue */
};
return 0;
}
void setup() {
PixelWidth = (CxMax - CxMin) / iXmax;
PixelHeight = (CyMax - CyMin) / iYmax;
/*create new file,give it a name and open it in binary mode */
fp = fopen(filename, "wb"); /* b - binary mode */
/*write ASCII header to the file*/
fprintf(fp, "P6\n %s\n %d\n %d\n %d\n", comment, iXmax, iYmax, MaxColorComponentValue);
}
void info() {
double distortion;
// widt/height
double PixelsAspectRatio = (double) iXmax / iYmax; // https://en.wikipedia.org/wiki/Aspect_ratio_(image)
double WorldAspectRatio = (CxMax - CxMin) / (CyMax - CyMin);
printf("PixelsAspectRatio = %.16f \n", PixelsAspectRatio);
printf("WorldAspectRatio = %.16f \n", WorldAspectRatio);
distortion = PixelsAspectRatio - WorldAspectRatio;
printf("distortion = %.16f ( it should be zero !)\n", distortion);
// file
printf("file %s saved. It is called M-bump-1.png in A Cheritat wiki\n", filename);
}
void close() {
fclose(fp);
info();
}
// ************************************* main *************************
int main() {
complex double c;
setup();
printf(" render = compute and write image data bytes to the file \n");
for (iY = 0; iY < iYmax; iY++)
for (iX = 0; iX < iXmax; iX++) { // compute pixel coordinate
c = give_c(iX, iY);
/* compute pixel color (24 bit = 3 bytes) */
compute_color(c, color);
/*write color to the file*/
fwrite(color, 1, 3, fp);
}
close();
return 0;
}
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.
Postprocessing
Convert, resize ( downsizing = subpixel accuracy) with Image Magic
convert n10000.ppm -resize 2000x2000 n2000.png
Items portrayed in this file
depicts
some value
4 October 2017
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 19:32, 4 October 2017 | 2,000 × 2,000 (808 KB) | Soul windsurfer | User created page with UploadWizard |
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File change date and time | 19:31, 4 October 2017 |