Vulcan #2

I am going to talk about math. Very simple math, do not be afraid. The Floor function, denoted $\lfloor x \rfloor$ is the largest integer less than or equal to x. So for example $\lfloor 1.2 \rfloor = 1$. There is also a function for the fractional part of a number. The actual name and symbol for this function are not well defined. (Often frac(x) or {x}). So I think it is safer to define it in terms of the floor function. $$ frac(x) = x - \lfloor x \rfloor$$ If you imagine a graph of this function is would gradually increase from 0 to 1 then immediately drop back to 0 and then repeat.

Now I can describe today's image. If (x,.y) are the pixel coordinates, then the image can be described as $$pixel.value = frac(y)$$ There is a lot left unsaid here. We are generating a number for each pixel on the screen. A little bit later we use the number as in index into a palette of colors to assign a color. In the formula, we are usng the y coordinate, so we get a smooth transition in the vertical direction from black to white (0 to 1), followed be a sharp drop back to black and the smooth rise again.