Bats and Butterflies

I’ve used butterfly-images to create fractals. Now I’ve found a butterfly-image in a fractal. The exciting story begins with a triabolo, or shape created from three isoceles right triangles:


The triabolo is a rep-tile, or shape that can be divided into smaller copies of itself:


In this case, it’s a rep-9 rep-tile, divisible into nine smaller copies of itself. And each copy can be divided in turn:


But what happens when you sub-divide, then discard copies? A fractal happens:

Fractal crosses (animated)


Fractal crosses (static)


That’s a simple example; here is a more complex one:

Fractal butterflies #1


Fractal butterflies #2


Fractal butterflies #3


Fractal butterflies #4


Fractal butterflies #5


Fractal butterflies (animated)


Some of the gaps in the fractal look like butterflies (or maybe large moths). And each butterfly is escorted by four smaller butterflies. Another fractal has gaps that look like bats escorted by smaller bats:

Fractal bats (animated)

Fractal bats (static)


Elsewhere other-posted:

Gif Me Lepidoptera — fractals using butterflies
Holey Trimmetry — more fractal crosses

Performativizing Papyrocentricity #50

Papyrocentric Performativity Presents:

Life LocomotesRestless Creatures: The Story of Life in Ten Movements, Matt Wilkinson (Icon 2016)

Heart of the MotherJourney to the Centre of the Earth: A Scientific Exploration into the Heart of Our Planet, David Whitehouse (Weidenfeld & Nicolson 2015)

LepidopterobibliophiliaBritish Butterflies: A History in Books, David Dunbar (The British Library 2012)

Minimal Manual – Georgisch Wörterbuch, Michael Jelden (Buske 2016)


Or Read a Review at Random: RaRaR

Performativizing Papyrocentricity #39

Papyrocentric Performativity Presents:

The Ogre by the Throat Extreme Eiger: The Race to Climb the Direct Route up the North Face of the Eiger, Peter and Leni Gillman (Simon & Schuster 2015)

Sing When You’re WingingButterflies and Moths in Britain and Europe, David Carter (Pan 1982)

Soul FeudThe Soul of the Marionette: A Short Enquiry into Human Freedom, John Gray (Penguin 2015)


Or Read a Review at Random: RaRaR