These are some small experiments with bitwise operations and trigonometric functions I made long time ago. The basic premise is that every pixel coordinate of the image, (i, j), is evaluated on a loop based on a formula using either bitwise operations, trigonometric functions, or a mix of both. This combination gives emergence to some surprising and very interesting patterns!

// Mod operations are also to prevent values going over 255,
// because the RGB range is [0, 255].
// (i, j) is every pixel coordinate in a loop.
int x = (i % 255) + (j % 255);
x %= 255;
int r = x % 255;
// Let's make use of the & bitwise operation.
int g = (x & i) % 255;
int b = (x & j) % 255; 
g.setColor(new Color(r, g, b));
g.drawRect(1024 - i,780 - j, 1, 1);

Here are some other interesting results:

This next one has some sort of a Moiré pattern, and also looks like a recursive or fractal structure. It has been feature in Paul Bourke’s wonderful fractal collection, and apparently different kind of mathematical methods give patterns very similar to this.

int x = (i * i) - (2 * (i | j)) + (j * j);
x %= 255;
x = Math.abs(x);
g.setColor(new Color(x, x, x));
g.drawRect(i, j, 1, 1);

Now, some really crazy patterns, perhaps some day I’ll tell you how these are generated ;-)

Finally there’s these small tiles, which are just a part of a larger previously generated pattern. But there’s just something so special about these, I can’t tell exactly why, but it surprises me that such a pattern can emerge from purely mathematical operations.