Moiré GIF: by Opal

My daughter started playing with moiré in procreate after I fiddled with it in a previous post. You know we breathe math in our home. She wanted to share:

Parallel to a Parabola

I received a question today about what curve is parallel to a parabola. I sat for a minute and realized that it wasn’t another parabola. It required parametric equations (at least if you wanted to keep it simple). That of course lead to code:

See the Pen jOqzMJb by Sophia (@fractalkitty) on CodePen.

The parametric equations for the parabola are:

  • x = 2at
  • y = at2

The parallel curve equations are:

  • x = 2at+ct/sqrt(1+t2)
  • y = at2 – c/sqrt(1+t2)


So I doodled and was pleasantly surprised when Sierpinski-like triangles formed. I am sure that a million people have discovered this before me, but I felt like I found a magic portal.

And that lead to coding (of which is currently a mess, and I will post later).

And one more version: