As I’ve shown pre-previously on Overlord-in-terms-of-issues-around-the-Über-Feral, you can create interesting fractals by placing restrictions on a point jumping inside a fractal towards a randomly chosen vertex. For example, the point can be banned from jumping towards the same vertex twice in a row, and so on.

But you can use other restrictions. For example, suppose that the point can jump only once or twice towards any vertex, that is, (j = 1,2). It can then jump towards the same vertex again, but not the same number of times as it previously jumped. So if it jumps once, it has to jump twice next time; and vice versa. If you use this rule on a pentagon, this fractal appears:

v = 5, j = 1,2 (black-and-white)

v = 5, j = 1,2 (colour)

If the point can also jump towards the centre of the pentagon, this fractal appears:

v = 5, j = 1,2 (with centre)

And if the point can also jump towards the midpoints of the sides:

v = 5, j = 1,2 (with midpoints)

v = 5, j = 1,2 (with midpoints and centre)

And here the point can jump 1, 2 or 3 times, but not once in a row, twice in a row or thrice in a row:

v = 5, j = 1,2,3

v = 5, j = 1,2,3 (with centre)

Here the point remembers its previous two moves, rather than just its previous move:

v = 5, j = 1,2,3, hist = 2 (black-and-white)

v = 5, j = 1,2,3, hist = 2

v = 5, j = 1,2,3, hist = 2 (with center)

v = 5, j = 1,2,3, hist = 2 (with midpoints)

v = 5, j = 1,2,3, hist = 2 (with midpoints and centre)

And here are hexagons using the same rules:

v = 6, j = 1,2 (black-and-white)

v = 6, j = 1,2

v = 6, j = 1,2 (with centre)

And octagons:

v = 8, j = 1,2

v = 8, j = 1,2 (with centre)

v = 8, j = 1,2,3, hist = 2

v = 8, j = 1,2,3, hist = 2

v = 8, j = 1,2,3,4 hist = 3

v = 8, j = 1,2,3,4 hist = 3 (with center)

Pre-previously on Overlord-in-terms-of-issues-around-the-Über-Feral, I looked at the fractals created when various restrictions are placed on a point jumping at random half-way towards the vertices of a square. For example, the point can be banned from jumping towards the same vertex twice in a row or towards the vertex to the left of the vertex it has just jumped towards, and so on.

Today I want to look at what happens to a similar point moving inside pentagons and hexagons. If the point can’t jump twice towards the same vertex of a pentagon, this is the fractal that appears:

Ban second jump towards same vertex (v + 0)

Ban second jump towards same vertex (color)

If the point can’t jump towards the vertex immediately to the left of the one it’s just jumped towards, this is the fractal that appears:

Ban jump towards v + 1

Ban jump towards v + 1 (color)

And this is the fractal when the ban is on the vertex two places to the left:

Ban jump towards v + 2

Ban jump towards v + 2 (color)

You can also ban more than one vertex:

Ban jump towards v + 0,1

Ban jump towards v + 1,2

Ban jump towards v + 1,4

Ban jump towards v + 1,4 (color)

Ban jump towards v + 2,3

And here are fractals created in similar ways inside hexagons:

Ban jump towards v + 0,1

Ban jump towards v + 0,3

Ban jump towards v + 0,1,2

Ban jump towards v + 0,1,2 (color)

Ban jump towards v + 0,1,4

Ban jump towards v + 0,1,5

Ban jump towards v + 0,2,4

Ban jump towards v + 0,2,4 (color)

Ban jump towards v + 1,2,3

Ban jump towards v + 1,2,3 (color)

Ban jump towards v + 1,2,4

Ban jump towards v + 1,2,4, (color)

Ban jump towards v + 1,3,5

Ban jump towards v + 1,3,5 (color)

Ban jump towards v + 1,2

Ban jump towards v + 1,2

Ban jump towards v + 1,3

Ban jump towards v + 1,3 (color)

Ban jump towards v + 1,5

Ban jump towards v + 1,5 (color)

Ban jump towards v + 2,3

Ban jump towards v + 2,3 (color)

Ban jump towards v + 2,4

Ban jump towards v + 2,4 (color)

Elsewhere other-accessible:

• Square Routes Re-Verticed