Rays in a square (moiré pattern)

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We are examining a moiré pattern which results from the following red and blue ray bundles.

$$p>0,k=1,...,p$$

$$y(x)=\frac{p}{k}\cdot x,y(x)=\frac{k}{p}\cdot xy(x)=\frac{p}{k}\cdot (x-1),y(x)=\frac{k}{p}\cdot (x-1)$$

The moiré pattern consists on the one hand of parabolas $y(x)=\frac{k}{p}\cdot x^2-\frac{k}{p}\cdot x$, and on the other hand of horizontals of the form $y=\frac{p}{k}$. Proof with the method of parameterised equations (Lattice-Geometry: “Indicial Equation Method”) (.html).

Manual superposition with SVG graphics of radial triangles (.html), simple rays (.html)

Principle sketch $(p=10)$ for the horizontal parallel shift $x\ge y$ (.pdf) (parabolas), $x<y$ (.pdf) (horizontals).

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