Here’s a set of three lines:

Three lines

Now try replacing each line with a half-sized copy of the original three lines:

Three half-sized copies of the original three lines

What shape results if you keep on doing that — replacing each line with three half-sized new lines — over and over again? I’m not sure that any human is yet capable of visualizing it, but you can see the shape being created below:

Morphogenesis #3

Morphogenesis #4

Morphogenesis #5

Morphogenesis #6

Morphogenesis #7

Morphogenesis #8

Morphogenesis #9

Morphogenesis #10

Morphogenesis #11 — the Hourglass Fractal

Morphogenesis of the Hourglass Fractal (animated)

The shape that results is what I call the hourglass fractal. Here’s a second and similar method of creating it:

Hourglass fractal, method #2 stage #1

Hourglass fractal #2

Hourglass fractal #3

Hourglass fractal #4

Hourglass fractal #5

Hourglass fractal #6

Hourglass fractal #7

Hourglass fractal #8

Hourglass fractal #9

Hourglass fractal #10

Hourglass fractal #11

Hourglass fractal (animated)

And below are both methods in one animated gif, where you can see how method #1 produces an hourglass fractal twice as large as the hourglass fractal produced by method #2:

Two routes to the hourglass fractal (animated)

Elsewhere other-engageable: