Some functions using the modulo-operation (mod, %, remainder) :

basic case: y=x%100, value waves between 0 and 99:

Additions:

addition of two different modulos: y=(x%100+x%79)/2

addition of three: y=(x%100+x%31+x%79)/3. I divide by n to get a result easier to compare, with f’(x)=1 when defined …

addition of four – and we’re approaching a fractal wave: y=(x%100 + x%79 + x%31 + x%17)/4

Subtract:

Subtracting two modulos: y=x%50 -x%30 – tops of the levels are horizontal e.g. f’(x)=0 when defined

and four y=x%50 -x%30 +x%20 -x%12, a ‘city skyline’-function

ZigZags:

A zigzag function: y=|x%(2*m)-m| : m= wave’s height, 2*m = wavelength:

In the javascript-demo I defined a special function for that:

function zigzag(x,m) {
return Math.abs(x%(2*m)-m);
}
adding two zigzags, y=zigzag(x,25) +zigzag(x,15):

… and three, y=zigzag(x,25) +zigzag(x,21)+zigzag(x,15), for a ‘random’ mountain silhuette:

small javascript-demo for testing (try also (x*x)%100 or the ‘barcode’-function: (x*x*x)%150-(x*x*x)%75 )

Pixel Bendel -code as an example of this in 2D, creating a ‘random’ size tiling: