Most people consider math boring, but sometimes it can be really beautiful. Recently I found some unusual application of Calcpad – to draw nice pictures using math formulas. In general, you can plot functions of two variables using the $Map command:

$Map{f(x;y) @ x = a : b & y = c : d}

I notices that you can get nice effects using the following types of functions:

f(x;y) = abs(cos(p1(x;y)) + cos(p2(x;y)) ...)

It creates families of intersecting curves that from canyons with hills in between. If you select “none” for the color scale, it creates nice and smooth pictures with shadows only. Bellow are some examples:

f(x;y) = abs(cos(x^2/10) + cos(y^2/10))

f(x;y) = abs(cos(x + y/3) + cos(x*y/7))

f(x;y) = abs(cos(x – sin(y)) + cos(y – sin(x)))

f(x;y) = abs(cos(r(x;y)*e^(ξ*r(x;y)))*e^(-1.5*ξ*r(x;y)))

f(x;y) = abs(cos(r(x;y)) + cos(y))

f(x;y) = abs(cos(x) + cos((y/4)^2))

f(x;y) = abs(cos(2*r(x;y)) + cos(x) + cos(y))

f(x;y) = abs(cos(2*r(cos(x/2);cos(y/2))))

f(x;y) = abs(r(cos(x/2);cos(y/2)))

In the above equations, r(x;y) = sqr(x^2 + y^2).

Download the latest Calcpad 3.2 and try to create your own pictures. Enjoy!

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