Color of a glider
I'm not sure what the objection to the sentence "Then the colour of a glider is the colour of its leading cell when it is in a phase which can be rotated or reflected to look like the above image." is.
(Note: I assumed that this section is a question that was answered by Nathaniel, and inserted some paragraph breaks to make it look neater. If it was a statement, not a question/answer, then sorry for the trouble. --Turtleguy1134 (talk) 15:21, 1 January 2015 (UTC))
It's not saying anything about whether or not the color changes when you reflect it, it's just saying that the color of this glider:
.X. X.. OXX
is the color of the cell marked "O", just like the color of this glider:
.X. ..X XXO
is the color of the cell marked "O". The sentence that is being edited is just a way of characterizing the eight different possible orientations of gliders -- with the reflections remark removed, there are four possible orientations of gliders whose color we haven't actually defined. Nathaniel 01:30, 14 April 2010 (UTC)
- However, the colour of this glider:
.X. X.. OXX
- is not the same as the colour of this glider: (they are travelling on opposite-parity diagonals; see for yourself)
X.. X.X OX.
- The two examples above are both travelling in the same direction, and are two generations away from each other.
- Your argument ignores the fact that the glider *flips over* every two generations, covering the sixteen images with just four orientations. Furthermore, introducing the reflection property actually creates a contradiction, as I demonstrated above.
- Finally, note that the definition on the Life Lexicon explicitly says 'rotated', and not 'rotated or reflected'. --Calcyman 17:41, 15 April 2010 (UTC)
- Just because it CAN be rotated, doesn't mean it SHOULD be rotated.
- The "That can be rotated part" just says that you are only allowed to calculate color (colour? No, I'm American) when it can be rotated to fit the picture. :However, when you are actually calculating the color you leave the glider as it is.
- I think.
- --Turtleguy1134 (talk) 15:21, 1 January 2015 (UTC)
The whole discussion about gliders is a bit hard to follow.
- sometimes gliders have british chromatics, other times, they are non-british.
- "the name is due in part to its glide symmetry;" wasn't that the totallity of the pun? How did the crystallographers come to choose that name? yet another pun?
- Crystallographically gliders have the symmetry of a color group - something on the order of the semidirect product of a translation group and a point group; in this case the eightfold dihedral group of the square. If this group had a one dimensional alternating irreducible representation, its character would be the colo(u)r. If there were two, we could have another adjective and another invariant.
Glide symmetry is named after the affine transformation known as glide-reflection, where a shape is reflected in a line of symmetry and translated parallel to that line. The composite transformation of two (identical) glide-reflections is an ordinary translation.
In three dimensions, it is possible for a "glide-rotation", where a shape is rotated around a helix. If the angle is an irrational multiple of pi, such as 1 radian, the shape will never appear in the same orientation twice. (This will never occur in a discrete cellular automaton, but may exist in an isotropic continuous environment.) Calcyman 09:24, 17 April 2010 (UTC)
- Sometimes I hate myself. For anyone reading this after the fact, calcyman is quite right. Nathaniel 15:24, 17 April 2010 (UTC)
Color and phase
It is in "win" phase that leading cell's color defines the color of a glider, yet that color is a minority in that phase. Sadly, this Wiki's markup won't let me show it in textual format. - Pooping Alien 09:23, 28 April 2012 (CDT)
- The code for fixed-width text is a leading space, FWIW:
.O. O.. XOX
- So yes, as we see here: two X, three O.
- It's probably just an issue of convenience (the glider's nose cell is the easiest to track, IMO) — but you can also note that within the glider's 3×3 bounding box, there are 5 cells of the "nose" parity and 4 of the other one. --Tropylium 12:02, 28 April 2012 (CDT)
- (BTW, shifted your sig from the heading to the body text; hope you don't mind)
The glider also works in B013568/S01, but in this rule it is a C/2 orthogonal spaceship instead. Evolve the Z-pentomino, the only pentomino to grow infinitely to see for yourself. Some of the gliders will be pulling tagalongs, like a duoplet. -wwei23 1:06 PM 9/23/2015 NY time
About how many gliders have been emitted since invention of Life? Just curious. -wwei23 1:59PM 9/27/2015 NY time