OFFSET
0,6
COMMENTS
The cellular automaton of A194270 contains a large number of distinct polygonal shapes. For simplicity we also call polygonal shapes "polygons".
In order to construct this sequence we use the following rules:
- Consider only the convex polygons and the concave polygons. Self-intersecting polygons are not counted. (Note that some polygons contain in their body a toothpick or D-toothpick with an exposed endpoint; that element is not a part of the perimeter of the polygon.)
- If two polygons have the same shape but they have different size then these polygons must be counted as distinct polygonal shapes.
- The reflected shapes of asymmetric polygons, both with the same area, must be counted as distinct polygonal shapes.
Question: Is there a maximal record in this sequence?
LINKS
EXAMPLE
Consider toothpicks of length 2 and D-toothpicks of length sqrt(2).
.
Stage New type Perimeter Area Term a(n)
. 0 - - - a(0) = 0
. 1 - - - a(1) = 0
. 2 - - - a(2) = 0
. 3 - - - a(3) = 0
. 4 hexagon 4*sqrt(2)+4 6 a(4) = 1
. 5 5.1 hexagon 2*sqrt(2)+8 8
. 5.2 octagon 4*sqrt(2)+8 14 a(5) = 1+2 = 3
. 6 pentagon 2*sqrt(2)+6 5 a(6) = 3+1 = 4
. 7 enneagon 6*sqrt(2)+6 13 a(7) = 4+1 = 5
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Omar E. Pol, Aug 23 2011
STATUS
approved