Beautiful corner case, very nice find.

(c) is good, prevent assignment to whoever has been oh-noer. Reasoning: Oh-noers can already exit, therefore oh-noers should drown and trigger traps.

Oh-noers should not descend to the bottom of the well, bypassing all water, and bomb holes in the bottom.

Need (b) too, apparently, ignore swimming ability when oh-noer enters water.

-- Simon

Quote from: Minim on August 16, 2019, 06:14:23 am

lemming is building a long stair and you have 5 builders, assign the builder five times to the lemming quickly and fast forward a couple of times, voila! Your long stair is completed!

Skill queueing like in Lix is a desired feature that I am totally 100% in for!

Lix queuing will affect physics. NL 12.6 requires one frame of shrugging between two builders; player may only re-assign builder during this shrugging frame. Queued builders will skip this frame. Replays with such queuing will fail on NL 12.6. All NL 12.6 replays will play perfectly in (NL with queuing).

Invalid skill assignments that were not wanted before and that are now distrupting solving replays.

First hunch is that this should fail fast and noisily. NL should refuse the replay when opening the file. Nastily, such early detection would require a complete physics simulation; also, viewer would get no information about what the problem is, and would have to guess.

Thus, I have no proposal yet.

I still believe that it is correct for NL to disallow two assignments during same physics update.

-- Simon

With regard to Lix specifically, which color tends to be the most visible? Perhaps every player should see their own lixes in that color?

Lovely idea for future projects. It would also obviate GUI to pick color. Fewer choices. I took (Player A's color on A's machine is same as player A's color on B's machine) unquestioned from physical board games.

I draw local player's lixes on top of everybody else's. Often, that's exactly want we want. Downside: Lone enemy attackers are invisible in an own dense crowd. Although (automatic color choices, local player gets best color) would have same problem.

I really don't think that's a good idea. Players tend to get attached to their favourite colours and want to keep playing as them

Yeah, I believe I don't want (fixed color that each local player uses for themself) in Lix.

#1 reason: people really care about the color. Raymanni even wants extra colors (8 -> 12) and would be happy to keep the player limit at 8; then, extra colors would be completely irrelevant to physics.

#2 reason: People in voicechat refer to other players by color. Opponents' colors must be clearly visible.

#3 reason: The replay format identifies teams by color.

#2 and #3 would work with server-side (for each team, fix a color across all machines). But since some color has to be picked and transmitted anyway, we can let the people pick it, they love it.

To be clear, this is mostly a solved problem for Lix, correct?

Right, unless Raymanni wants extra colors. Mainly, I wanted to write about the abstract problem, less about Lix.

Hard to imagine how you'd do better for 8 with rainbow + black & white. Basically the 8 corners of the RGB-space cube.

Neither the 1-metric nor the 2-metric in the RGB cube agree with the human visibility metric. Red (255, 0, 0) and black (0, 0, 0) are 255 apart and are clearly distinguishable. Bright green (0, 255, 0) and bright cyan (0, 255, 255) are also 255 apart, but far less disginguishable than red and black.

Sorry for late answers! More on ccx's ideas later.

-- Simon

Christmas tree problem

You have a fir tree and want to decorate it with christmas lights.



The fir tree's green bushy "surface" is cone-shaped, with a circular boundary at the bottom.



You also have n candles. These are about to be placed on the fir tree.

In reality, the candles would be connected by electrical cable, which would restrict the candles' distribution on the tree. Assume that the candles need no electricity, or that the cable between any two candles is arbitrarily long.



Task. Distribute the n candles on the fir tree such that the candles are nicely spaced apart from all other candles. You may place candles on the boundary.

Precisely: Given a distribution D of the candles, compute the minimum of all distances d(k, k') between all candles k ≠ k' of D. We call this minimum f(D). We want to maximize f. Thus, denote by M the supremum of the minimum distances of all distributions, M = sup { f(D) : D is a distribution }. Finally, find an arrangement of the candles D that attains f(D) = M. If no such arrangement exist, instead find a sequence (D_i) of arrangements such that the sequence of minimums f(D_i) converges to M.

In a variations of the christmas tree problem, you're encouraged to avoid the boundary, too. Then, for each distribution, don't merely compute the minimum of all candle-to-candle distances, but also the minimum of all candle-to-boundary distances, and use the minimum of these two minimums. Across all distributions, maximize this value.

Example. Given only one candle, put it anywhere you like. If you'd like to avoid the boundary, too, then put the lone candle at the top of the tree.

Example. Given two candles, even if distance to the boundary doesn't matter, the best distribution depends on the shape of the cone. If the cone is very tall and thin, put one candle at the top and one on the circular boundary at the bottom. Otherwise, if the cone is squat and low-risen, put both candles on opposite points of the boundary.

Example. If your christmas tree is not a tree at all, but rather the unbounded real line, you can space the candles arbitrarily far from each other. This is very nice.



Application. If your christmas tree is instead the space of all colors, and you have 8 Lix player colors, find a distribution of 8 colors such that no two colors look more similar than necessary. This is hard, especially if you, in addition, want to avoid black because black lixes looks too much like the boundary level background.

End. The christmas tree problem is really about abstract metric spaces, not christmas trees, but christmas trees inspired me to first think about this problem in detail. I don't know whether this problem is known by other names in mathematics. I don't know whether it's more common to avoid the boundary or not.

-- Simon

I think all of these forum captchas are solvable by robots, and higher difficulty merely makes it annoying for humans.

I found no link to prove claim. I'm fine trying the difficult captcha until I find proof that the difficulty doesn't hinder robots.

It's good style to change the security question frequently.

-- Simon

-- Simon

This will be fixed in 0.9.29. Observers will start zoomed out to see the entire map.

-- Simon