# Tri + Eye = Troculus

Troculus, a fractal Lovecraftian entity created by dividing-and-discarding parts of a triangle

Troculus converted into a circle

Troculus switching between forms (animated gif)

Elsewhere Other-Accessible…

Circus Trix — how to create Troculus & Co.

# Six Mix Trix

Here’s an equilateral triangle divided into six smaller triangles:

Equilateral triangle divided into six irregular triangles (Stage #1)

Now keep on dividing:

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Equilateral triangle dividing into six irregular triangles (animated)

But what happens if you divide the triangle, then discard some of the sub-triangles, then repeat? You get a self-similar shape called a fractal:

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Triangle fractal (animated)

Here’s another example:

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Triangle fractal (animated)

You can also delay the divide-and-discard to create a more symmetrical fractal, like this:

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Triangle fractal (animated)

What next? You can use trigonometry to turn the cramped triangle into a circle:

Triangular fractal

Circular fractal
(Open in new window for full image)

Triangle-to-circle (animated)

Here’s another example:

Triangular fractal

Circular fractal

Triangle-to-circle (animated)

And below are some more circular fractals converted from triangular fractals. Some of them look like distorted skulls or transdimensional Lovecraftian monsters:

(Open in new window for full image)

Previous Pre-Posted

Circus Trix — an earlier look at sextally-divided-equilateral-triangle fractals

# Loricifera Rising

The very Lovecraftian Loriciferan Pliciloricus enigmaticus (Higgins & Kristensen, 1986)

N.B. The title of this incendiary intervention is a paronomasia on Kenneth Anger’s film Lucifer Rising (1972) (which I ain’t never seen nohow).

# The Call of Cthuneus

Cuneiform, adj. and n. Having the form of a wedge, wedge-shaped. (← Latin cuneus wedge + -form) (Oxford English Dictionary)

This fractal is created by taking an equilateral triangle and finding the centre and the midpoint of each side. Using all these points, plus the three vertices, six new triangles can be created from the original. The process is then repeated with each new triangle (if the images don’t animate, please try opening them in a new window):

If the centre-point of each triangle is shown, rather than the sides, this is the pattern created:

Triangles in which the sides are divided into thirds and quarters look like this:

And if sub-triangles are discarded, more obvious fractals appear, some of which look like Lovecraftian deities and owl- or hawk-gods: