Re:Illegal prime
by fizx on Monday January 11, 2010 @03:18PM
(#1045898)
Think about Gödel numbering or Cantor diagonalization.
Let's assume discrete, rectangular representations of images (width, height in pixels and colorspace of #000000-#FFFFFF). Here's an injective mapping from natural numbers (the indices of the vector of images) to actual images:
# In a C-like language where ** is
# the exponentiation operator, and
# ints are unbounded.
int colors = 0xFFFFFF + 1;
int i = 0;
vector images = new vector();
while(i++) {
for(int width = 1; width < i; width++) {
int height = i - width;
int area = width * height;
int pixels[area];
int combinations = colors ** area;
for(int c = 0; c < combinations; c++) {
for(int p = 0; p < area; p++) {
pixels[p] = c % (colors ** (p + 1));
}
images.append(new image(width, height, pixels));
}
}
}
Let's assume discrete, rectangular representations of images (width, height in pixels and colorspace of #000000-#FFFFFF). Here's an injective mapping from natural numbers (the indices of the vector of images) to actual images: