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Playing with primes
Posted by Erik on Oct 18 2005 @ 23:48 :: 4367 unique visits
This is an interresting image created by the following code:
CODE: C
int main(int argc, char* argv[])
{
const int width = 1024;
const int height = 768;
int num = width * height;
unsigned char* data = new unsigned char[num * 3];
memset(data, 0, num * 3);
for (int n = 2; n < num; n++)
{
int i, t;
for (i = 2; (t = (n * i)) < num; i++) {
int t3 = t * 3;
#define opp(a) data[t3+a] += 2
opp(0);
opp(1);
opp(2);
}
}
makebmp(data, width, height);
return 0;
}
{
const int width = 1024;
const int height = 768;
int num = width * height;
unsigned char* data = new unsigned char[num * 3];
memset(data, 0, num * 3);
for (int n = 2; n < num; n++)
{
int i, t;
for (i = 2; (t = (n * i)) < num; i++) {
int t3 = t * 3;
#define opp(a) data[t3+a] += 2
opp(0);
opp(1);
opp(2);
}
}
makebmp(data, width, height);
return 0;
}
Previously I used this code to calculate prime numbers. Now I was playing with it and found this interresting image. The program starts with an all black image, then loops through all pixels (which have their own numer) and increment all the pixels which numers are a multiple of the current pixel.
So for pixel 2 pixels 2, 4, 6, 8, ... get their color value incremented by 2.
And for pixel 25 pixels 25, 50, 75, 100, ... get their color values incremented.
Everyone knows prime numers aren't realy predictable but in this image you can see some interresting non prime white lines. Every pure black pixel is a prime, only with the jpg encoding this isn't realy acurate anymore.
30 comments posted so far
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2. On Oct 20 2005 @ 20:56 schabbs wrote:
that's pretty cool. i'm in a intro c++ course right now and wanted to play with it alittle though and i'm wondering what you had for include files. thanx3. On Oct 20 2005 @ 21:26 Erik wrote:
You needCODE: CPP
#include <windows.h> // for the BITMAPFILEHEADER and BITMAPINFOHEADER structures
#include <stdio.h> // for the fopen/fwrite/fclose functions
#include <stdio.h> // for the fopen/fwrite/fclose functions
And makebmp() is just a simple function I wrote:
CODE: CPP
void makebmp(unsigned char* data, int width, int height)
{
FILE *file;
BITMAPFILEHEADER BitmapFileHeader;
BITMAPINFOHEADER BitmapInfoHeader;
file = fopen("out.bmp", "wb");
if (file == NULL)
return;
BitmapFileHeader.bfSize = sizeof(BITMAPFILEHEADER);
BitmapFileHeader.bfType = 0x4D42;
BitmapFileHeader.bfReserved1 = 0;
BitmapFileHeader.bfReserved2 = 0;
BitmapFileHeader.bfOffBits = sizeof(BITMAPFILEHEADER) + sizeof(BITMAPINFOHEADER);
BitmapInfoHeader.biSize = sizeof(BITMAPINFOHEADER);
BitmapInfoHeader.biPlanes = 1;
BitmapInfoHeader.biBitCount = 24;
BitmapInfoHeader.biCompression = BI_RGB;
BitmapInfoHeader.biSizeImage = width * height * 3;
BitmapInfoHeader.biXPelsPerMeter = 0;
BitmapInfoHeader.biYPelsPerMeter = 0;
BitmapInfoHeader.biClrUsed = 0;
BitmapInfoHeader.biClrImportant = 0;
BitmapInfoHeader.biWidth = width;
BitmapInfoHeader.biHeight = height;
fwrite(&BitmapFileHeader, sizeof(BITMAPFILEHEADER), 1, file);
fwrite(&BitmapInfoHeader, sizeof(BITMAPINFOHEADER), 1, file);
fwrite(data, BitmapInfoHeader.biSizeImage, 1, file);
fclose(file);
}
{
FILE *file;
BITMAPFILEHEADER BitmapFileHeader;
BITMAPINFOHEADER BitmapInfoHeader;
file = fopen("out.bmp", "wb");
if (file == NULL)
return;
BitmapFileHeader.bfSize = sizeof(BITMAPFILEHEADER);
BitmapFileHeader.bfType = 0x4D42;
BitmapFileHeader.bfReserved1 = 0;
BitmapFileHeader.bfReserved2 = 0;
BitmapFileHeader.bfOffBits = sizeof(BITMAPFILEHEADER) + sizeof(BITMAPINFOHEADER);
BitmapInfoHeader.biSize = sizeof(BITMAPINFOHEADER);
BitmapInfoHeader.biPlanes = 1;
BitmapInfoHeader.biBitCount = 24;
BitmapInfoHeader.biCompression = BI_RGB;
BitmapInfoHeader.biSizeImage = width * height * 3;
BitmapInfoHeader.biXPelsPerMeter = 0;
BitmapInfoHeader.biYPelsPerMeter = 0;
BitmapInfoHeader.biClrUsed = 0;
BitmapInfoHeader.biClrImportant = 0;
BitmapInfoHeader.biWidth = width;
BitmapInfoHeader.biHeight = height;
fwrite(&BitmapFileHeader, sizeof(BITMAPFILEHEADER), 1, file);
fwrite(&BitmapInfoHeader, sizeof(BITMAPINFOHEADER), 1, file);
fwrite(data, BitmapInfoHeader.biSizeImage, 1, file);
fclose(file);
}
4. On Oct 23 2005 @ 21:44 predominant wrote:
How long did it take you to execute this? I can imagine that it perhaps would have talen a few minutes to complete?5. On Oct 23 2005 @ 23:04 Erik wrote:
It doesn't even take a minute on my system (Athlon 64 3000+). But the program runs in O(n^2) so increasing the image size will increase the time it takes by twice as much.6. On Oct 24 2005 @ 17:14 guest wrote:
Might be interesting to provide download link for .bmp or .tiff to eliminate the problems with .jpg compression.7. On Oct 24 2005 @ 22:26 guest wrote:
those lines are 'n % 2 = 0', but still very nice idea!8. On Jul 21 2008 @ 04:44 guest wrote:
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1. On Oct 19 2005 @ 13:42 dustin wrote:
I did this sort of thing, only using the decimal places of pi and then giving a higher value a lighter color image (i.e. 6 is lighter than 2). I didn't come up with anything too great though, and I really maxed out php by only going ~5,300 decimal places.http://aerno.com/pi/