\\ move forward
move(z) = {
	my (x=real(z), y=imag(z));
	forstep (k=1+max(#binary(x), #binary(y)), 2, -1,
		my (w=2^k, m=2^(k-1)-1, zz=x%w + (y%w)*I);
		if (zz==m*(1+I),     return (z+1),
		    zz==(m+1)*(1+I), return (z-1),
			zz==m-1+(m+1)*I, return (z-I),
			zz==m+2+m*I,     return (z+I)
		);
	);
	if (y%2==0,
		if (x%2==0, z+1, z+I),
		if (x%2==0, z-I, z-1)
	);
}

\\ move backward
moveb(z) = {
	my (x=real(z), y=imag(z));
	forstep (k=1+max(#binary(x), #binary(y)), 2, -1,
		my (w=2^k, m=2^(k-1)-1, zz=x%w + (y%w)*I);
		if (zz==m*(1+I)+1,     return (z-1),
		    zz==(m+1)*(1+I)-1, return (z+1),
			zz==m-1+(m+1)*I-I, return (z+I),
			zz==m+2+m*I+I,     return (z-I)
		);
	);
	if (y%2==0,
		if (x%2==0, z+I, z-1),
		if (x%2==0, z+1, z-I)
	);
}

{
	z=0;
	for (n=0, oo,
		print (n " " real(z));
		if (imag(z)==128, break);
		z=moveb(z);
	);
}

quit