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Reverse engineer video game function/formula

Paul Loht
Posted 4 years ago
POSTED BY: Paul Loht
6 Replies
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Paul Loht
Paul Loht
Posted 4 years ago
POSTED BY: Paul Loht
Jim Baldwin
Jim Baldwin
Posted 4 years ago

That's close but it doesn't work for all 18 sample points.

Show[Plot[{91 - n + Floor[(n - 1)/4]}, {n, 1, 18}], ListPlot[data[[All, 3]]]]

Prediction of dx
POSTED BY: Jim Baldwin

How about this:

data = {90, 89, 88, 87, 86, 86, 85, 84, 84, 83, 82, 81, 81, 80, 80, 79, 78, 78};

Show[
 Plot[{91 - n + Floor[(n - 1)/4]}, {n, 1, 10}],
 ListPlot[data]]

enter image description here
POSTED BY: Gustavo Delfino
Paul Loht
Paul Loht
Posted 4 years ago

Hi Jim,

I noticed the stairstep appearance, but I haven’t found a function yet which would produce the inconsistent height.

I have been thinking that plotting the values along an x, y, and z axis might reveal something, but I haven’t figured out how to do that yet. It sounds like a stretch anyway.

I had assumed that keeping y constant would simplify deriving how dx decreased as x increased, but it sounds like you’re saying that may obscure the solution.

I’ll give that a try, in the meantime, thanks for the tip.
POSTED BY: Paul Loht
Jim Baldwin
Jim Baldwin
Posted 4 years ago

Use ListPointPlot3D:

data = {{1100, 1000, 90, 100}, {1200, 1000, 89, 110}, {1300, 1000, 88, 120}, {1400, 1000, 87, 130},
   {1500, 1000, 86, 140}, {1600, 1000,  86, 150}, {1700, 1000, 85, 160}, {1800, 1000, 84, 170}, 
   {1900, 1000, 84, 180}, {2000, 1000, 83, 190}, {2100, 1000, 82, 200}, {2200, 1000, 81, 210},
   {2300, 1000, 81, 220}, {2400, 1000, 80, 230}, {2500, 1000, 80, 240}, {2600, 1000, 79, 250},
   {2700, 1000, 78, 260}, {2800, 1000, 78, 270}};
ListPointPlot3D[data[[All, {1, 2, 3}]]]

But with y being constant, it's not a very interesting display.

And my point about needing y to vary is that IF the formula depends on y you can't get there from here if y doesn't vary. It might end up that y isn't used at all in the formula but one can't know that either without varying y.
POSTED BY: Jim Baldwin
Jim Baldwin
Jim Baldwin
Posted 4 years ago

The data given only has y=1000 so you can't expect to find out the effect of y. You can only (potentially) determine the formula for dx as a function of x given that y=1000.

But you can get some pretty strong hints as to some of the features of the function by plotting the data.

ListPlot[data[[All, {1, 3}]], Frame -> True, FrameLabel -> {"x", "dx"}]

Plot of x vs dx

The slopes of neighboring points seem to take on just two values: 0 and -0.1. Also, the intercepts change by +1 every once in a while.

LinearModelFit[data[[#[[1]] ;; #[[2]], {1, 3}]], x, x]["BestFitParameters"] & /@
 {{1, 5}, {6, 8}, {9, 12}, {13, 14}, {15, 17}}
(* {{101., -0.01}, {102., -0.01}, {103., -0.01}, {104., -0.01}, {105., -0.01}} *)

Show[ListPlot[(data[[#[[1]] ;; #[[2]], {1, 3}]] & /@ {{1, 5}, {6, 8}, {9, 12}, {13, 14}, {15, 17}}),
   Frame -> True, FrameLabel -> {"x", "dx"}],
 ListPlot[(data[[#[[1]] ;; #[[2]], {1, 3}]] & /@ {{1, 5}, {6, 8}, {9, 12}, {13, 14}, {15, 17}}),
   Joined -> True]]

x vs dx with line segments joined
POSTED BY: Jim Baldwin
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