I am trying to create a specific type of colour map for some data. The data is in the form of a list with dimensions 300000 x 3, that is 300,000 sets of {x, y, n} where x and y are basically the $xy$ cartesian coordinates and n is a value either 0 or 1. Doing a list plot of the 300,000 points gives the following figure:

enter image description here

What I am trying to make is a colour map of this figure, that is made up of 5 x 5 evenly sized squares (so 25 all up), in which the colour-key denotes the mean of the n values of all the points within that square. Is this possible?

Please let me know if any additional information is needed,


1 Answer 1

data = Join[RandomReal[1, {300000, 2}], RandomChoice[{0, 1}, {300000, 1}], 2];

{300000, 3}

nbins = 5;
binlims = Through[{Floor[Min@#, .01] &, Ceiling[Max@#, .01] &}@#] & /@ Transpose[data];
{xbins, ybins} = {##, -Subtract[##]/nbins} & @@@ Most[binlims];
binlists = BinLists[data, xbins, ybins, {0, 2, 2}];
binmeans =  Flatten /@ Map[Mean, binlists[[All, All, All, All, -1]], {-2}];

cft = Charting`FindTicks[{0, nbins}, {0, 1}];
MatrixPlot[binmeans, DataReversed -> True, ColorFunction -> "Rainbow",
  FrameTicks -> {{cft, cft}, {cft, cft}}]

enter image description here

With nbins = 25 we get

enter image description here

  • $\begingroup$ I take it that if I would like to increase the number of squares, I just alter that 5 in the second line? Also, I tried changing it to 25 and it looks good, but there are a lot of data ticks. Is it possible to maybe only show every second, or even third data tick? $\endgroup$
    – Lagiacrus
    Feb 27, 2018 at 18:38
  • $\begingroup$ @Lagiacrus, right; changing 5 changes the number of bins. Re ticks, please see the updated version. $\endgroup$
    – kglr
    Feb 27, 2018 at 20:17
  • $\begingroup$ So far the code appears to have been working well, but I just tried it for a similar situation in which the third element of the list can be either 0, 1, 2 or 3 (instead of the original 0 or 1) and in this case the binmeans never ends up with a value higher than 1. Is there a limit on the value that binmeans can take? $\endgroup$
    – Lagiacrus
    Mar 3, 2018 at 12:57
  • $\begingroup$ @Lagiacrus, you can change {0, 2, 2} in the definition of binlists to {0,, 4, 4} if the third list can take values in {0,1,2,3}. $\endgroup$
    – kglr
    Mar 3, 2018 at 14:00

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