Plot a list of matrices at heights in 3d scatter plot

Question

I have a file with a number of matrices separated by a newline. I can plot any one of these matrices as a heatmap as shown in http://gnuplot.sourceforge.net/demo/heatmaps.html

However, now I would like to visualize all the matrices together on the same graph by plotting each matrix at increasing values of z, where each point is a coloured dot. I am trying to achieve something similar to the following question,

Plot 3D Grid Data as Heat Map using gnuplot

but without the cubes, as dots are sufficient.

This is the data for one matrix:

 7.606193E-01 -2.706752E-01  1.605924E-01  9.973101E-01  6.646065E-01 -4.177295E-01 -5.101588E-01 -5.338852E-01 -9.443505E-01  6.273689E-01  4.401633E-01  9.428387E-01 -1.783963E-01  1.702644E-01 -9.304313E-01  3.995178E-01 
-1.574189E-01 -3.911715E-01 -5.581077E-01 -3.719385E-02  7.144460E-01 -3.147125E-01  4.237802E-01  6.533050E-01  5.385187E-01  8.391651E-02 -5.773817E-01  1.456075E-01  6.028832E-01  5.313966E-01  3.894490E-01  7.329324E-01 
 8.147309E-01 -8.286917E-01 -9.708381E-01 -6.634787E-02  8.603123E-01  8.952920E-01  6.777392E-01  4.347730E-01 -9.271995E-01  8.899992E-01  5.525438E-01 -7.496139E-01  7.592094E-01  3.412833E-01  1.220876E-01  7.281239E-01 
 6.915789E-01  3.365000E-01 -4.771788E-01  7.674200E-01  8.059295E-01  3.545558E-01  2.764826E-01  3.801301E-01 -6.679796E-01  1.163551E-01 -5.292152E-01 -3.500514E-01 -8.614216E-01 -8.356531E-02 -8.391827E-01  7.258298E-01 
 1.219247E-01  5.344889E-01  8.977039E-01 -5.708083E-01 -6.809624E-01 -5.687558E-01  3.830947E-01  9.990373E-01 -6.038938E-01  9.162573E-01 -4.214753E-01  4.186414E-01 -4.224649E-01 -9.376176E-01 -1.170071E-01  3.825447E-01 
-1.046988E-01  5.206562E-01 -9.832160E-01 -6.588389E-01  6.122716E-01  2.926736E-01 -8.736564E-01  9.977460E-01  8.937872E-01 -8.719974E-02 -7.742046E-01 -9.490100E-01  6.090313E-01  8.220433E-01  7.705420E-01  5.937839E-01 
 8.668659E-01 -5.811435E-01 -4.980876E-01 -5.458175E-02 -1.702000E-01 -9.681295E-01 -9.898823E-01  8.014537E-01  6.852101E-01  3.412942E-01 -4.313660E-01  6.886256E-01 -8.974125E-01  8.012120E-01  7.893018E-01 -1.869330E-01 
-1.168977E-01 -8.988775E-01 -2.580437E-01 -8.019403E-02  4.935626E-01  3.774684E-01  5.609375E-02  8.018482E-01 -9.803250E-01 -8.223162E-01 -7.441623E-02  7.592162E-01 -3.084599E-01  2.728176E-01 -7.114622E-01 -4.335231E-01 
 9.071215E-01  7.551532E-01  1.640213E-02 -2.627113E-01 -1.102158E-01 -3.576760E-02  7.584369E-02  3.586933E-01  9.412469E-01 -7.919924E-01 -7.883645E-01 -4.693788E-01 -1.549372E-01  1.823575E-01  4.206510E-01 -4.489097E-01 
 2.449895E-01 -4.566137E-02  5.805491E-01  3.808071E-01  4.885185E-01  9.662528E-01 -9.306209E-02  2.467101E-02  2.380986E-01 -9.053143E-01 -3.499831E-01 -4.224079E-01 -2.420047E-01  1.568254E-01 -1.696076E-01 -2.344714E-01 
-1.045739E-01 -2.254802E-01 -5.760012E-01  7.194423E-01  9.792110E-01 -7.514746E-01 -1.239218E-01 -3.922474E-01 -6.499553E-01  5.908898E-01  8.695512E-01 -6.576686E-01  7.101708E-01  6.389254E-01 -3.228182E-01  3.177363E-01 
-7.059239E-01 -8.482834E-01 -1.630977E-01 -9.891499E-01 -5.450270E-01 -6.303106E-01  1.596098E-01 -2.695453E-01  1.340886E-01 -3.888265E-01 -4.888381E-02  1.609239E-01  3.058087E-01  7.288026E-01  9.176123E-01  2.593470E-02 
-5.400585E-01  8.222967E-01  3.648388E-01 -6.635013E-01 -4.210275E-01 -2.741717E-01  1.431661E-01 -2.184412E-01 -6.006791E-01 -9.289613E-03  2.788451E-01 -2.769694E-01 -9.857075E-01 -5.143206E-01 -1.455316E-01  9.782214E-01 
-7.254217E-01 -1.668047E-01 -7.403084E-01  5.606276E-01  1.713349E-01  8.025852E-01 -9.133063E-01 -3.648469E-01  9.402033E-01 -2.317766E-01  7.771178E-01  8.427679E-01  5.951350E-02  9.725678E-01  7.514953E-01 -2.132574E-02 
 3.962623E-01 -8.680837E-01 -6.393657E-01  7.831294E-01 -5.947012E-02 -9.781432E-01 -8.829182E-01 -9.939770E-01  7.487056E-02 -7.578757E-01  6.196460E-01 -7.909356E-01 -1.149577E-01 -2.736676E-01  2.013560E-01  5.961972E-02 
 7.165400E-01 -2.371667E-01 -7.857778E-01  7.715441E-01  5.449374E-01  2.804987E-02 -1.380231E-01 -5.877602E-01  3.679530E-01  3.016719E-01 -5.242305E-01  1.064826E-01 -6.910435E-02  7.062310E-01  8.472682E-02 -9.717143E-01 

Answer 1

I am not sure if I understood correctly, but it seems that you want each matrix as a heatmap at a fixed (arbitrary) z-value.

As mentioned on the link you posted, making a plot like that one would require (at least to my knowledge) a lot of scrambling around on gnuplot. However, you could have a rough idea by doing:

set term png
set out "tmp.png"

set view 80,30

splot "tmp" matrix u 1:2:(2):3 w p pt 5 ps 0.75 pal,\
      "tmp" matrix u 1:2:(1):3 w p pt 5 ps 0.75 pal,\
      "tmp" matrix u 1:2:(0):3 w p pt 5 ps 0.75 pal

Which would give you:

Not pretty, but works. You'd have to play around with the labels, tics and view parameters depending on how many matrices you have. Hope it helps!