W = 100
T = matrix(2*W+1, 2*W+1)
flip(z) = (T[real(z)+W+1,imag(z)+W+1]++)%2

{
	z = 0;
	dir = 1;
	count = 0;
	for (n=0, 10 000,
		print (n " " count);
		if (flip(z),
			\\ white square
			count++;
			dir /= (1+I),
			\\ black square
			count--;
			dir *= (1+I)
		);
		dir /= gcd(real(dir), imag(dir));
		z += dir;
	);
}

quit