It’s a classic of low literature:

There was a young man of Devizes
Whose balls were of different sizes:
     The one was so small
     ’Twas no use at all;
But t’other won several prizes.

But what if he had been a young man with balls of different colours? This is a core question I want to interrogate issues around in terms of the narrative trajectory of this blog-post. Siriusly. But it’s not the keyliest core question. More corely keyly still, I want to ask what a fractal phallus might look like. Or a phrallus, for short. The narrative trajectory initializes with this fractal, which is known as a pentaflake (so-named from its resemblance to a snowflake):

Pentaflake — a pentagon-based fractal

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It’s created by repeatedly replacing pentagons with six smaller pentagons, like this:

Pentaflake stage 0

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Pentaflake stage 1

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Pentaflake stage 2

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Pentaflake stage 3

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Pentaflake stage 3

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Pentaflake stage 4

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Pentaflake (animated)

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Pentaflake (static)

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This is another version of the pentaflake, missing the central pentagon of the six used in the standard pentaflake:

No-Center Pentaflake stage 0

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No-Center Pentaflake stage 1

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Stage 2

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Stage 3

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Stage 4

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No-Center Pentaflake (animated)

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No-Center Pentaflake (static #1)

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No-Center Pentaflake (static #2)

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The phrallus, or fractal phallus, begins with an incomplete version of the first stage of the pentaflake (note balls of different colours):

Phrallus stage 1

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Phrallus stage 1 (monochrome)

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Phrallus stage 2

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Phrallus stage 3

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Stage 4

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Stage 5

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Stage 6

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Stage 7

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Stage 8

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And there you have it: a fractal phallus, or phrallus. Here is an animated version:

Phrallus (animated)

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Phrallus (static)

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But the narrative trajectory is not over. The center of the phrallus can be rotated to yield mutant phralloi. Stage #1 of the mutants looks like this:

Phrallus (mutation #1)

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Phrallus (mutation #2)

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Phrallus (mutation #3)

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Phrallus (mutation #4)

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Phrallus (mutation #5)

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Mutant phralloi (rotating)

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Here are some animations of the mutant phralloi:

Phrallus (mutation #3) (animated)

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Phrallus (mutation #5) (animated)

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This mutation doesn’t position the pentagons in the usual way:

Phrallus (another upright version) (animated)

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The static mutant phralloi look like this:

Phrallus (mutation #2)

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Phrallus (mutation #3)

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Phrallus (upright #2)

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And if the mutant phralloi are combined in a single image, they rotate like this:

Mutant phralloi (rotating)

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Coloured mutant rotating phralloi #1

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Coloured mutant rotating phralloi #2

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