After about a year, I found the answer:
CGImageRef CGGenerateNoiseImage(CGSize size, CGFloat factor) CF_RETURNS_RETAINED {
NSUInteger bits = fabs(size.width) * fabs(size.height);
char *rgba = (char *)malloc(bits);
srand(124);
for(int i = 0; i < bits; ++i)
rgba[i] = (rand() % 256) * factor;
CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceGray();
CGContextRef bitmapContext = CGBitmapContextCreate(rgba, fabs(size.width), fabs(size.height),
8, fabs(size.width), colorSpace, kCGImageAlphaNone);
CGImageRef image = CGBitmapContextCreateImage(bitmapContext);
CFRelease(bitmapContext);
CGColorSpaceRelease(colorSpace);
free(rgba);
return image;
}
This effectively generates a noise image that is guaranteed to be random and can be drawn using the code from Jason Harvig's answer.
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