For $\lambda$ real, we consider the pattern given by the value modulo 2 of the integer part of $\lambda(x^2+y^2)$, where $(x,y)\in\Z\times\Z$. We study the periodicity and other geometric properties of this pattern, and show that it can provide, by visual inspection and an elementary computation, a diophantine approximation for $\lambda$. We conclude with similar results for other moduli.
"Fresnel zones on the screen." Experiment. Math. 2 (4) 301 - 309, 1993.