Monteverde’s Mathemorphosis

Here are some fractals based on the Angelo di Monteverde or Angelo della Resurrezione carved by the Italian sculptor Giulio Monteverde (1837-1917) for the monumental cemetery of Staglieno in Genoa.

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

A fractal based on an angel carved by Giulio Monteverde

Jug is the Drug

In “The Gems of Rebbuqqa”, I interrogated notions around the concept of priestesses who permanently juggle three giant eye-like gems, a ruby, a sapphire, and an emerald, atop a sandstone altar. In “The Schismatarch” (forthcoming), I will interrogate notions around the concept of a Himalayan sect that believes this universe is one of three juggled by a god called Nganāma. Each of these universes contains a smaller Nganāma who juggles three dwarf universes; et sic ad infinitum. Moreover, the Nganāma juggling our universe sits in a larger universe, one of three juggled by a giant Nganāma in a larger universe still, which is one of three on a higher plane; et sic ad infinitum. The cosmology of the Nganāma-sect is fractal: ut supra, sic infra: as above, so below. Here are some animated gifs inspired by these two stories and based on juggled eye-gem fractals.

A fractal of three juggled blue eyes

 A fractal comprising three juggled eyes

A fractal of three sets of three juggled eyes

A fractal comprising three sets of three sets (sic) of three juggled eyes

A fractal based on juggled eyeballs

A fractal of three juggled eyes, in front of each of which three more eyes are juggled

A fractal of 27 juggled eyes

A Feast of Fractiles

A rep-tile is a shape that can be divided into copies of itself. One of the simplest rep-tiles is the equilateral triangle, which can be divided into four copies of itself, like this:

Self-dividing equilateral triangle

If, on the other hand, the triangle is subdivided and then one of the copies is discarded, many interesting fractals can be made from this very simple shape:

Fractal triangle creating Sierpinski gasket

Triangle fractal 2

This sequence illustrates how a more complex fractal is created:

Triangle fractal 3 split image 1

Triangle fractal 3 split image 2

Triangle fractal 3 split image 3

Triangle fractal 3 split image 4

Triangle fractal 3 split image 5

Triangle fractal 3 split image 6

Triangle fractal 3 split image 7

Triangle fractal 3 split image 8

And here is the sequence in a single animated gif:

Triangle fractal 3

Triangle fractal 4

Triangle fractal 5

Triangle fractal 6

Triangle fractal 7

Triangle fractal 8

Triangle fractal 9

Triangle fractal 10

Triangle fractal 11

Triangle fractal 12

Triangle fractal 13

Triangle fractal 15

Triangle fractal 16

Triangle fractal 17

Triangle fractal 18

Triangle fractal 19

Triangle fractal 20

Triangle fractal 21

Triangle fractal 22

Triangle fractal 23

Triangle fractal 24

Triangle fractal 25

Triangle fractal 26