Improve readme

[mattneub]

The README is inaccurate about the significance of the turtle (and therefore the spectre); it makes it sound as if the turtle is merely another tile that behaves just like the hat, which is not at the all the case. This PR, at the cost of some additional verbiage, is more accurate.

[christianp]

Thanks for this!

[julescubtree]

I believe the update in this PR is incorrect. From everything I've read,

• the hat only tiles the plane with its reflection (README is correct)
• the turtle is in the same family as the hat, so it only tiles with its reflection (README is incorrect)
• the spectre is not a turtle with curved edges. The spectre tile with straight edges can tile periodically with its reflection, or aperiodically without its reflection. A spectre with curved edges forces reflections not to be used. (README is incorrect)

This January 2024 article (by one of the co-authors of the original hat and spectre papers) states clearly that

• the hat and turtle is are in the same family (see the section that says that hat is Tile(1,√3) and the turtle is Tile(√3,1))
• Tile(1,1) tiles periodically with reflection, and aperiodically without reflection; the modified Tile(1,1) with curves is the spectre

@christianp I'd like to submit a PR reverting this change to what I believe is correct, but not without giving @mattneub the opportunity to chime in first.

[mattneub]

@julescubtree Thanks for the courtesy! I've no axe to grind here. My contribution was based on what I saw as confusion in the original wording. It was based on my best efforts after research. If you think my summary is wrong, do by all means correct it.

[julescubtree]

@mattneub Thanks for replying! I'm basically coming from the same place as you, I think, trying to get things as clear and accurate as possible based on my understanding.

@christianp I'll go ahead and write a PR to correct things per my understanding, and will strive for the clarity that Matt brought.

[christianp]

Thanks for that PR, @julescubtree. I also initially thought the original PR was incorrect, but somehow convinced myself it was right. Playing with the interactive tool, I think I thought that the straight-edged spectre $(a,b) = (1,1)$ was the turtle, which is incorrect: the turtle is $(\sqrt{3},1)$.

I'll accept #10.