In the previous post I showed some identicons that happened to be symmetrical due to the underlying math of modulo arithmetic. Here we'll generate symmetrical designs explicitly using mirroring.
To start, let's pick an arbitrary curve by rotating through 90° at equal intervals and choosing random radii:
Then we can reflect that curve across the x-axis:
and that curve across the y-axis:
Additionally, we can pick a curve that rotates through 180° and only reflect it across one axis. Here's a sample of shapes created by reflecting a 90° curve across the x- and y-axes, or a 180° curve reflected across the x-axis:
Just a shape with a color is a bit indistinct, so let's pick a second shape to overlay:
Since one shape can be within the boundary of the other, I have made sure the narrower or shorter one in front. Alternatively, we can show the shape underneath cutting a hole in the top shape:
To me several of these are evocative of natural, technological, and religious imagery. Since we're choosing radii on a continuous spectrum, the possibility space is all but infinite, and it's multiplied three times over by the choice of three different shapes. If you have ideas for further variations, email me.
In the final post of this series, we'll explore another shape-generating function.