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shmageggy

I would describe this as multiplicative rather than logarithmic. 2×2×2×2...

Or maybe exponential if you consider your score to be 2^(number of walls you've jumped).

I don't get logarithmic, though.

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I think the term is "geometric"

Geometric is the same as exponential. It is just a geometric interpretation instead of algebraic.

Pedantically,

    s_n = k (-1)^n

for

    n = 0, 1, 2, ...

and nonzero constant k is a non-constant geometric sequence that doesn't exhibit exponential behavior.

This is the exponential function, 2^x. Where the independent variable is the number of walls jumped. For instance, after 30 jumps, your score/tile reads 1073741824, or 2^30.

Or it's the logarithmic function lg(x), where the independent variable is the score and the dependent variable is roughly proportional to the number of times you've clicked.

Well yes, logbase2(x), where x is your score, does equal the number of wall jumps. But that doesn't account for how the game is laid out. Your score is a result of the number of jumps you've made. The number of jumps you've made is not the result of your score. Therefore, despite these two functions being the inversely related, the correct relationship is 2^x. That is just my opinion though.

I agree "exponential" would have been a more natural choice.

"Therefore, despite these two functions being the inversely related, the correct relationship is 2^x."

There is no "correct relationship", there is a relationship that (depending on choice of variables) we can describe as y=2^x or y=lg(x).

Sure, score = 2^walls iff log_2(score) = walls. So, being equivalent statements, one alone can not be correct.

However, as you said, one choice of describing the relationship is certainly more natural. The exponential description assigns a score to every natural number. While the logarithmic description does not.

I would interpret correct in the way that it is sometimes said, "the correct way to think about X is..." which doesn't say other ways of thinking are wrong, but limited or not illuminating.

After around 4096 it starts tapering off, hence logarithmic.

I chose the name without any thought, really.

An early version of the code did use log2() on the score internally, but now it does pow(2) externally.

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