Interference Patterns in Multiplication

[pinballpsycho]

Not exactly a brot, but drawing lines from points on a circle representing a multiplicand to points representing the product will generate these interference patterns.

The interference patterns might remind you of the shape of the primary bulbs in generalized Mandelbrots.  I'll post a link in a comment to an explanation given by the Mathologer.

<a href="https://vimeo.com/moogaloop.swf?clip_id=194995145&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">https://vimeo.com/moogaloop.swf?clip_id=194995145&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

[pinballpsycho]

Mathologer's link:

<a href="https://www.youtube.com/v/qhbuKbxJsk8&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/qhbuKbxJsk8&rel=1&fs=1&hd=1</a>

[hgjf2]

Not exactly a brot, but drawing lines from points on a circle representing a multiplicand to points representing the product will generate these interference patterns.

The interference patterns might remind you of the shape of the primary bulbs in generalized Mandelbrots.  I'll post a link in a comment to an explanation given by the Mathologer.

So models having the waves of water into rounded cauldron after several reflections.

[pinballpsycho]

Kind of, but instead of waves crisscrossing as they radiate, these patterns are simple lines interfering with one another as they're drawn from multiplicands to their products. each represented by points on the perimeter of a circle.  Continuously shifting the value of the multiplier creates the illusion.  I modified (bastardized) the approach slightly by drawing the lines from an inner circle to an outer one, and projecting them beyond the screen boundary.  I wanted the effect to be more immersive.