Added Harmony Reflection

[miyucomics]

Adds a reflection for the golden ratio. It seems fitting because there is a pattern for pi and a separate one for tau, so why not one for phi.

[vgskye]

1.618033988749895 :3

[miyucomics]

I only added three decimal places because of Hex's double tolerance, but I realize that you could probably scale it up to get more digits. I'll update it.

[Alwinfy]

honestly with how easy this is to compute (5 0.5 pow 1 add 0.5 mul) i don't feel great about this taking up a whole pattern slot; pi/tau are in the stdlib [why is tau in the stdlib?] because they're transcendental and very annoying to approximate.

is there a specific use-case you have for this? would you be willing to let this be a scribe's refl. easter egg? [read off a gold item]

[miyucomics]

There are (virtually) infinite pattern slots, right? I know phi is easy to compute, but so is e via its Taylor series and that made it into the standard library. Tau is there, I assume because it's the more "pure" circle constant, and pi is there, I assume because people don't want to have to do tau 2 div each time. By that logic, why not phi too? It's mechanically trivial to compute, yes, but noisy in context when you look over a hex and have to lexiconize 5 0.5 pow 1 add 0.5 mul as "the patterns that push the golden ratio." It saves players the operations it would take to calculate that number by just having it as a reflection.

I'd actually say that e has fewer gameplay applications than phi for most people. Phi is nice for geometry. I wanted to add it because I was working on a little project (scattering points evenly across a sphere using the Fibonacci sphere technique in order to send raycasts off in all directions) and the golden ratio as a readily-accessible pattern would have been really helpful. There is also the more famous use of sunflower-like configurations, spiral tilings, and phyllotaxis. Even if phi isn't frqeuently used, it's just a nice number that encapsulates a nice idea.

Sure, one could work around it by embedding or computing it but that is so much overhead for a constant that could just be baked in. The pull request is already here, it isn't competing with any more useful patterns, it saves op counts like Dioscuri's Gambit, and it might nudge players towards some fun uses. There isn't any harm I see in including it and the upside is small and sweet.

[miyucomics]

I would be interested in making it a Scribe's Reflection Easter egg and I could add that too if people like it enough (golden apple maybe? Sunflower?), but I think it still would be a nice pattern on its own. The pie Easter egg for example doesn't come with any numbers that you yourself can't use the Arc Reflection for.

[miyucomics]

Question about PRing: should I be running datagen and pushing the altered datagen cache files?

[miyucomics]

Hmm, I thought if I just git rm them, it would note that my PR never actually needed to track these files and stop tracking the .cache files that are preventing a clean merge.

[PoolloverNathan]

looks good, but some minor formatting nitpicks (and the description)

[PoolloverNathan]

• description probably needs some work (tentative description suggested; what does the golden ratio do again?)
• I'd unquote phi (and e) for consistency
• other greek letters aren't italicized

Suggested change

	"e": "Adds $(italic)e/$, the base of natural logarithms, to the stack.",
	"phi": "Adds $(italic)φ/$, the ratio of a whole to its greater part, to the stack.",
	e: "Adds $(italic)e/$, the base of natural logarithms, to the stack.",
	phi: "Adds φ, the golden ratio, to the stack.",

[PoolloverNathan]

Suggested change

	"e": "Euler's Reflection",
	"phi": "Harmony Reflection",
	e: "Euler's Reflection",
	phi: "Harmony Reflection",

[object-Object]

Question about PRing: should I be running datagen and pushing the altered datagen cache files?

Ideally you should do a rebase to remove cef485d and undo your datagen changes in 41371c1, then rebase onto main. We just removed the datagen cache files in #906.

[object-Object]

honestly with how easy this is to compute (5 0.5 pow 1 add 0.5 mul) i don't feel great about this taking up a whole pattern slot; pi/tau are in the stdlib [why is tau in the stdlib?] because they're transcendental and very annoying to approximate.

is there a specific use-case you have for this? would you be willing to let this be a scribe's refl. easter egg? [read off a gold item]

I have a specific use case: my Entity Cannon hex uses golden-section search, and a phi pattern would make that a bit simpler.

https://github.com/object-Object/hex-hexes/blob/4326f0c041292927a2780c89117c1ca9e61af4dc/macros/Entity_Cannon.hexpattern#L413