Modulo rugs of 3D functions

mAnasa-taraMgiNI

Consider a 3D function $latex z=f(x,y)$. Now evaluate it at each point of a $latex n times n$ integer lattice grid. Compute $latex z mod n$ corresponding to each point and plot it as a color defined by some palette that suits your aesthetic. The consequence is a what we term the “modulo rug”.
For example, below is a plot of $latex z=x^2+y^2$.

matrixmod01_318Figure 1: $latex z=x^2+y^2, n=318$

We get a pattern of circles around a central circular system reminiscent of ogdoadic arrangements in various Hindu maṇḍala-s. From the aesthetic viewpoint, the best modulo rugs are obtained with symmetric functions higher even powers — this translates into some pleasing symmetry in the ru. Several examples of such are shown below.

matrixmod06_318Figure 2: $latex z=x^4-x^2-y^2+y^4, n=318$

matrixmod08_315Figure 3: $latex z=x^4-x^2-y^2+y^4, n=315$

matrixmod13_309Figure 4: $latex z= x^6-x^4-y^4+y^6, n=309$

matrixmod12_318Figure 5: $latex z=x^6-x^2-y^2+y^6, n=318$

matrixmod07_312Figure 6: $latex z=x^4-x^2+y^2-y^4, n=310$

All the above $latex…

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sudhasarathi61

It is absolutely clear that this world and its contents are purely mental and nothing solid in it. To come out of suffering entirely you should know your mind thoroughly.

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