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The UUDDUUD sequence, or the 3/7th sequence

Posted 9 years ago
POSTED BY: Ed Pegg
6 Replies

I've added the Demonstration Semigraceful Eulerian Graphs for exploring these objects.

enter image description here

POSTED BY: Ed Pegg

Nice Demonstration, Ed !

POSTED BY: Vitaliy Kaurov

The Scotty Dog Graph

Graph[#[[1]] \[DirectedEdge] #[[2]] & /@ 
Partition[FoldList[Plus, 0,  Flatten[Table[2 IntegerDigits[73, 2] - 1, {9}]] Range[63]], 2, 1]]

Scotty Dog Graph

Here are some of the more interesting weave generation numbers:

weaving numbers

POSTED BY: Ed Pegg

I think the Uud's were on Doctor Who (maybe spelled Ood).

Ed, I find this unusual. Is there a reason for this sequence?

Here is a version with a single graphic (so it is easier to annotate with arrows):

texts = MapIndexed[Text, 
  Table[7 n (n - 1)/2 + If[OddQ[n], {0, 4, 5}, {5, 4, 0}], {n, 1, 
    10}], {2}];
FindNextNumbers[Text[n_, {x_, y_}], texts_, dx_] := 
 Select[texts, Abs[#[[1]] - n] == dx &]

list = Module[{dx = 5}, 
  Most[NestWhileList[
     With[{choices = FindNextNumbers[#, Flatten[texts], ++dx]},
       Switch[Length[choices], 0, None,
        1, choices[[1]],
        _, Print["error ",Length[choices]]; None]] &, 
     texts[[1, 3]], # =!= None &]][[All, 2]]];

Graphics[{texts, {Red, Arrow /@ Partition[list, 2, 1]}}]

enter image description here

Of course, I wonder about other chess move sequences.

POSTED BY: Todd Rowland

Ed, is UUDDUUD is some known thing, what does it stand for? Also what is a "king move"? Is this post only for mathematicians on an average person can understand this?

POSTED BY: Sam Carrettie

The start is 4, 5, 7, 4, 0, 5, 11, 4 ... up 1, up 2, down 3, down 4, up 5, up 6, down 7. +1, +2, -3, -4, +5, +6, -7. ++--++- ... UUDDUUD.

In Chess, a King moves one space in any direction.

To understand the grid below, all that is needed is to understand subtraction and moving a space.

King grid

POSTED BY: Ed Pegg
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