OFFSET
0,1
COMMENTS
From Andrey Zabolotskiy, Jun 24 2017: (Start)
a(n) counts the points that can be obtained through combining points and lines starting from a square and applying n operations from the set of 7 operations called Huzita-Justin Axioms (HJA) which model origami foldings, namely:
1. Given two points p1 and p2, we can fold a line connecting them
2. Given two points p1 and p2, we can fold p1 onto p2
3. Given two lines l1 and l2, we can fold l1 onto l2
4. Given a point p1 and a line l1, we can make a fold perpendicular to l1 passing through p1
5. Given two points p1 and p2 and a line l1, we can make a fold that places p1 onto l1 and passes through the point p2
6. Given two points p1 and p2 and two lines l1 and l2, we can make a fold that places p1 onto line l1 and places p2 onto line l2
7. Given a point p1 and two lines l1 and l2, we can make a fold perpendicular to l2 that places p1 onto line l1
A crossing of two lines (folds) is a new point, automatically.
Different sequences of HJA operations can lead to the same set of points and lines, so this sequence gives an upper combinatorial estimate of the number of points accessible after n HJA operations. Actual number of accessible points is much less.
(End)
REFERENCES
R. J. Lang, Origami approximate geometric constructions, in Tribute to a Mathemagician, Peters, 2005, pp. 223-239.
LINKS
R. J. Lang, Origami and geometric constructions
Wikipedia, Huzita-Hatori axioms
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 11 2006
EXTENSIONS
Name and offset edited by Andrey Zabolotskiy, Jun 24 2017
STATUS
approved