Math Art with Calcpad

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:

circles-and-hyperbolas
f(x;y) = abs(cos(x^2/10) + cos(y^2/10))
unsymmetric-hyperbolas
f(x;y) = abs(cos(x + y/3) + cos(x*y/7))
zig-zag-tiles
f(x;y) = abs(cos(x – sin(y)) + cos(y – sin(x)))
concentric-waves
f(x;y) = abs(cos(r(x;y)*e^(ξ*r(x;y)))*e^(-1.5*ξ*r(x;y)))
intersecting-parabolas
f(x;y) = abs(cos(r(x;y)) + cos(y))
intersecting-parabolas-x
f(x;y) = abs(cos(x) + cos((y/4)^2))
puzzle
f(x;y) = abs(cos(2*r(x;y)) + cos(x) + cos(y))
buttons
f(x;y) = abs(cos(2*r(cos(x/2);cos(y/2))))
pins
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!

Published by Calcpad

Hi, my name is Ned. I am a structural engineer with over 20 years of experience in the design of nuclear and industrial facilities, factories, residential and public buildings. I am a fan of engineering, mathematics and computer programming. I spend a lot of time for developing of useful tools that help structural design.

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