# Making a Moire pattern animation

I'm trying to animate a pattern I made. I made this on a graphing website called Desmos, but ran into problems making all the lines move. Apparently it's too computationally difficult for the website I was using. I have the mathematical equations. How would I animate this? Is it possible to animate?

The equations I used are:

$$e^{ST\log(x)}+e^{ST\log(y)}=1$$

$$e^{ST\log(1-x)}+e^{ST\log(y)}=1$$

$$e^{ST\log(x)}+e^{ST\log(1-y)}=1$$

$$e^{ST\log(1-x)}+e^{ST\log(1-y)}=1.$$

$$x$$ and $$y$$ are numbers between $$0$$ and $$1.$$

$$S$$ is a list of numbers that gauges the spacing of the curves. I used $$49$$ $$S$$ values to generate a total of $$392$$ evenly spaced curves along the diagonals of the squares (see image).

$$S= \{15.3039,10.3612,7.9153,6.3793,5.3019,4.4955,3.8656,3.3584,2.9405,2.5903,2.2926,2.0367,1.8146,1.6204,1.4496,1.2983,1.1638,1.04377,.93622,.83959,.75256,.67401,.603,.53871,.48045,.42762,.37969,.33619,.29673,.26094,.22852,.19917,.17265,.14874,.12722,.10791,.090664,.075316,.061733,.049793,.039383,.030399,.0227475,.0163414,.0111008,.0069525,.0038286,.0016664,.0004081 \}.$$

$$T$$ is a "slider" between $$0$$ and $$2$$ that continuously transitions the curves over time through the ambient space.

Here is a frozen image at $$T_1:$$

• Can you give some details re the ranges of x, y, S and T. – batFINGER Mar 10 '19 at 12:45