In the posts “Boole(b)an #1″ and “Boole(b)an #2” I looked at fractals created by certain kinds of ban on a point jumping (quasi-)randomly towards the four vertices, v=1..4, of a square. For example, suppose the program has a vertex-history of 2, that is, it remembers two jumps into the past, the previous jump and the pre-previous jump. There are sixteen possible combinations of pre-previous and previous jumps: [1,1], [1,2], 1,3] … [4,2], [4,3], [4,4].
Let’s suppose the program bans 4 of those 16 combinations by reference to the current possible jump. For example, it might ban [0,0]; [0,1]; [0,3]; [2,0]. To see what that means, let’s suppose the program has to decide at some point whether or not to jump towards v=3. It will check whether the combination of pre-previous and previous jumps was [3+0,3+0] = [3,3] or [3+0,3+1] = [3,4] or [3+0,3+3] = [3,2] or [3+2,3+0] = [1,3] (when the sum > 4, v = sum-4). If the previous combination is one of those pairs, it bans the jump towards v=3 and chooses another vertex; otherwise, it jumps towards v=3 and updates the vertex-history. This is the fractal that appears when those bans are used:
ban = [0,0]; [0,1]; [0,3]; [2,0]
And here are more fractals using a vertex-history of 2 and a ban on 4 of 16 possible combinations of pre-previous and previous jump:
ban = [0,0]; [0,1]; [0,3]; [2,2]
ban = [0,0]; [0,2]; [1,0]; [3,0]
ban = [0,0]; [0,2]; [1,1]; [3,3]
ban = [0,0]; [0,2]; [1,3]; [3,1]
ban = [0,0]; [1,0]; [2,2]; [3,0]
ban = [0,0]; [1,1]; [1,2]; [3,2]
ban = [0,0]; [1,2]; [1,3]; [3,2]
ban = [0,0]; [1,2]; [2,3]; [3,2]
ban = [0,0]; [1,3]; [2,2]; [3,1]
ban = [0,1]; [1,3]; [2,3]; [3,3]
ban = [0,1]; [0,2]; [2,0]; [3,3]
ban = [0,1]; [0,2]; [3,0]; [2,0]
ban = [0,1]; [0,3]; [1,0]; [2,2]
ban = [0,1]; [0,3]; [1,0]; [3,3]
ban = [0,1]; [0,3]; [1,1]; [1,2]
ban = [0,1]; [0,3]; [1,2]; [3,2]
ban = [0,1]; [0,3]; [2,0]; [2,2]
ban = [0,1]; [1,1]; [1,2]; [2,2]
ban = [0,2]; [1,1]; [2,0]; [3,3]
ban = [0,2]; [1,1]; [2,2]; [3,3]
ban = [0,2]; [1,1]; [3,0]; [3,3]
ban = [0,2]; [1,2]; [1,3]; [2,2]
ban = [0,2]; [1,2]; [1,3]; [3,1]
ban = [0,2]; [1,2]; [1,3]; [3,2]
ban = [0,2]; [1,2]; [2,0]; [2,2]
ban = [0,2]; [1,2]; [2,0]; [3,1]
ban = [0,2]; [1,2]; [2,0]; [3,2]
ban = [0,2]; [1,2]; [2,1]; [2,2]
ban = [0,2]; [1,2]; [2,1]; [2,3]
ban = [0,2]; [1,2]; [2,2]; [2,3]
ban = [0,2]; [1,2]; [3,2]; [3,3]
ban = [0,2]; [1,3]; [2,0]; [2,3]
ban = [0,2]; [1,3]; [2,0]; [3,1]
ban = [0,2]; [1,3]; [2,2]; [3,1]
ban = [0,2]; [2,0]; [2,1]; [2,3]
ban = [0,2]; [2,1]; [2,2]; [2,3]
ban = [0,2]; [2,1]; [2,2]; [3,1]
ban = [0,2]; [2,1]; [3,1]; [3,2]
ban = [0,2]; [2,2]; [3,1]; [3,3]
ban = [0,3]; [1,0]; [1,1]; [2,0]
ban = [0,3]; [1,0]; [1,1]; [2,1]
ban = [0,3]; [1,0]; [1,1]; [2,2]
ban = [0,3]; [1,0]; [1,1]; [3,0]
ban = [0,3]; [1,0]; [3,0]; [3,3]
ban = [0,3]; [1,1]; [1,2]; [3,2]
ban = [0,3]; [1,1]; [2,1]; [2,3]
ban = [0,3]; [1,1]; [2,1]; [3,1]
ban = [0,3]; [1,2]; [3,2]; [3,3]
ban = [0,3]; [1,3]; [2,1]; [2,3]
ban = [0,3]; [2,0]; [3,1]; [3,3]
ban = [0,3]; [2,2]; [3,0]; [3,1]
ban = [1,0]; [1,1]; [1,2]; [3,1]
ban = [1,0]; [1,1]; [2,2]; [3,0]
ban = [1,0]; [1,1]; [3,0]; [3,1]
ban = [1,0]; [1,1]; [3,0]; [3,3]
ban = [1,0]; [1,2]; [3,0]; [3,2]
ban = [1,0]; [1,3]; [3,0]; [3,1]
ban = [1,0]; [2,1]; [2,3]; [3,0]
ban = [1,0]; [2,1]; [3,0]; [3,1]
ban = [1,1]; [1,2]; [2,1]; [3,2]
ban = [1,1]; [1,2]; [2,3]; [3,2]
ban = [1,1]; [1,2]; [2,3]; [3,3]
ban = [1,1]; [1,2]; [3,2]; [3,3]
ban = [1,1]; [2,0]; [2,1]; [3,1]
ban = [1,1]; [2,0]; [2,2]; [3,3]
ban = [1,1]; [2,1]; [2,3]; [3,3]
ban = [1,1]; [2,3]; [3,0]; [3,3]
ban = [1,2]; [1,3]; [2,0]; [3,1]
ban = [1,2]; [1,3]; [2,1]; [3,2]
ban = [1,3]; [2,0]; [2,2]; [3,1]
ban = [1,3]; [2,1]; [2,3]; [3,1]
ban = [1,3]; [3,0]; [3,2]; [3,3]
Elsewhere other-engageable
Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral 