Demos Noise! (Part 31)

@charlesvattimo4674 11 months ago

I have a group of functions that I'd like you to show off if you still do your cool graphs series. Firstly, f = cos^2(i), where i is all values of x divisible by a given factor, represented in the upward staircase i = -mod(x , d) + x, where d is a sliding variable from one multiple of pi to another in steps of pi/10. However, these bounds are offset by a tiny amount, between +1/100 and +1/1000; this is critical in making anything more interesting than constant slopes. Secondly, F = sum(n=1 to i) of function f. Zoom out to the scale of thousands to see multiple sine curves of steps, though each step is tiny, more like individual points. If d is set to a whole multiple of pi plus the tiny offset, there will only be one rising sine wave whose crests are more or less tangent to the slope y=x. These rising sine waves made up of points can be replicated with the function of x*cos^2( x/d * [the tiny offset of d's bounds] +- [a multiple of pi]/10 ). Finally, you can add in the sin equivalent of these equations to double the density of steps to create smoother curves, as the points of the sin sums will be placed at the midpoints of the empty spaces between each wave. I am honestly enamored by how the maths of these functions can create something so cool and interconnected, especially how if you were to replace i with x, all you'd get is a useless mass of vertical lines all falling under the slope of y=x. I hope you check out these functions, feel free to experiment with it, see if it makes some interesting sounds too.