# Performativizing Papyrocentricity #43

Papyrocentric Performativity Presents:

Avens AboveHarrap’s Wild Flowers: A Guide to the Wild Flowers of Britain & Ireland, Simon Harrap (Bloomsbury 2013)

Place of GladesA Dictionary of British Place-Names, A.D. Mills (Oxford University Press 1991)

De Minimis Curat Rex?Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander (Oneworld 2014)

Seen and Not HeardThe Greatest Albums You’ll Never Hear, ed. Bruno MacDonald (Aurum Press 2014)

Or Read a Review at Random: RaRaR

# He Say, He Sigh, He Sow #31

“SSV are not the Sisters. Their official full name is SSV-NSMABAAOTWMODAACOTIATW. Could this possibly stand for ‘Screw Shareholder Value — not so much a band as another opportunity to waste money on drugs and ammunition, courtesy of the idiots at Time Warner’? Surely not. That would require a comma.” — Andrew Eldritch.

Create a triangle. Find a point somewhere inside it. Choose a corner at random and move halfway towards it. Mark the new point. Repeat the procedure: choose, move, mark. Repeat again and again. In time, a fractal will appear:

However, if you try the same thing with a square – choose a corner at random, move halfway towards it, mark the new point, repeat – no fractal appears. Instead, the points fill the interior of the square:

But what happens if you impose restrictions on the randomly chosen corner (or chorner)? Suppose you can’t choose the same corner twice in a row. If this rule is applied to the square, this fractal appears:

Now apply the no-corner-twice-in-a-row rule to a square that contains a central chorner. This fractal appears:

And if the rule is that you can choose a corner twice in a row but not thrice? This fractal appears:

Here is the rule is that a corner can’t be chosen if it was chosen two moves ago:

But what if the restriction is based not on how often or when a corner is chosen, but on its proximity, i.e. how near it is to the marked point? If the nearest corner can’t be chosen, the result is the same as the no-corner-twice-in-a-row rule:

But if the second-nearest corner can’t be chosen, this fractal appears:

This is the fractal when the third-nearest corner can’t be chosen:

And this is the fractal when the fourth-nearest, or most distant, corner can’t be chosen:

Here are the same restrictions applied to a pentagon:

Nearest corner forbidden

Second-nearest corner forbidden

Third corner forbidden

Fourth corner forbidden

Fifth corner forbidden

Fifth corner forbidden (animated)

And a pentagon with a central chorner:

Now try excluding more than one corner. Here are pentagons excluding the n-nearest and n+1-nearest corners (for example, the nearest and second-nearest corners; the second-nearest and third-nearest; and so on):

But what if the moving point is set equal to the n-nearest corner before it moves again? If the corner is the second-nearest and the shape is a triangle with a central chorner, this is the fractal that appears:

Animated version

And here is the same rule applied to various n-nearest corners in a pentagon: