Endless pattern based on prime numbers

Hi, Habr! One morning, I had the idea to find an " exclusive OR " between the coordinates of a point in space and check the resulting number for simplicity. The result of such a simple algorithm you can see in the picture. More under the cut.

Pattern Generation Algorithm

Algorithm in C ++

longlong temp = x ^ y; // x и y координаты точки// Далее идет проверка temp на простоту одним из алгоритмов.// Например алгоритм Бэйли-Померанс-Селфридж-Вагстафф (BPSW) проверки n на простотуif(isprime(temp) == true) { 
// рисуем закрашенную точку
} else {
// оставляем точку пустой
}

This algorithm gives the following endless patterns:


You can also watch video with patterns:

Other designs

If you replace the XOR operation ( XOR ) with the operation OR or AND , you can get fractal triangles:



You can also use any other checks instead of checking for a prime number, for example, division without remaining a certain number. But such options give less varied patterns.

Program and source

To test the pattern generator, I wrote a simple program that can be downloaded along with the source here . To work with images using the library OpenCV.