gnuplot: plot 2d heatmap with non-integer pixel coordinates, with image pixels produces rotated 3D plot

You may need to clarify exactly what you want, and what you know in advance about your data properties. For now I suggest you might try this and see if it comes close to what you intended:

set size ratio -1    # make sure that a square is really a square
unset key
set palette cubehelix negative
set pointsize 10     # adjust if needed to make the pixels touch
plot 'foo' using 1:2:3 with points pointtype 5 fillcolor palette

You could also use the plotting style with boxxyerror to plot your heatmap (check help boxxyerror). If you have a regular grid and you don't want to manually tune the box size to get a fully colored area you can let gnuplot extract the minimum step size in x and y automatically.

Script:

### 2D heatmap with boxxyerrors and automatic boxsize
reset session

$Data <<EOD
0.9882380255806047 0.9882380255806047 -0.7703887858517308
0.9882380255806047 0.9929170035354357 -0.03247814980870606
0.9882380255806047 0.9975959814902666 -0.6944306255482046
0.9882380255806047 1.0022749594450977 -0.746165843927831
0.9882380255806047 1.0069539373999286 -0.5151139695781666
0.9882380255806047 1.0116329153547596 -0.1838806386646351
0.9929170035354357 0.9929170035354357 -0.7703887858517308
0.9929170035354357 0.9975959814902666 -0.9227715329230436
0.9929170035354357 1.0022749594450977 -0.9171361902702745
0.9929170035354357 1.0069539373999286 -0.7797704881116272
0.9929170035354357 1.0116329153547596 -0.6650103546953546
0.9975959814902666 0.9975959814902666 -0.7703887858517308
0.9975959814902666 1.0022749594450977 -0.9065086173718683
0.9975959814902666 1.0069539373999286 -0.3481667020388293
0.9975959814902666 1.0116329153547596 0.10123715036482903
1.0022749594450977 1.0022749594450977 -0.7703887858517308
1.0022749594450977 1.0069539373999286 -0.28406345548617745
1.0022749594450977 1.0116329153547596 0.1835875555217213
1.0069539373999286 1.0069539373999286 -0.7703887858517308
1.0069539373999286 1.0116329153547596 -0.4920684723609338
1.0116329153547596 1.0116329153547596 -0.7703887858517308
EOD

# find the smallest dx,dy > 0
stats $Data u ($0==0?(x0=$1,y0=$2):0, dx=abs(x0-$1), dx==0 ? NaN : dx) : \
              (dy=abs(y0-$2), dy==0 ? NaN : dy) nooutput
dx = STATS_min_x/2.
dy = STATS_min_y/2.

set palette rgb 33,13,10
set size ratio -1
set style fill solid 1.0
set key noautotitle

plot $Data u 1:2:(dx):(dy):3 w boxxy palette
### end of script

Result:

Addition:

Just for completeness, the automatic search for dx,dy>0 in the above script would fail with the data in the example below. The data below is (especially chosen) such that even if you (alternatively) compare the difference of two successive x (or y) values to find the minimum dx and dy it would fail. Hence you need a bit more effort.

• plot the data into the temporary datablock $Temp by using the option smooth freqency (check help smooth frequency). With this you get unique values in ascending order. Do this for x-column and y-column.
• since the sorted data for x and y in $Temp will be separated by two empty lines, you can address it via index (check help index).
• use stats to calculate the difference between successive data points in $Temp and get the minimum in the variable STATS_min.

Script:

### 2D heatmap with boxxyerrors and automatic boxsize
reset session

$Data <<EOD
  1   3   1.5
  1   5   1.9
  3   1   3.1
  5   4   5.7
  5   1   5.1
  3   4   3.7
  1   4   1.7
  4   4   4.7
  4   1   4.1
  4   3   4.5
  4   5   4.9
  1   1   1.1
  5   3   5.5
  5   5   5.9
  3   3   3.5
  3   5   3.9
EOD

# find the smallest dx,dy > 0
set table $Temp
    plot $Data u 1:0 smooth freq
    plot $Data u 2:0 smooth freq
unset table
v1 = NaN
stats $Temp u (v0=v1,v1=$1,dv=v1-v0) index 0 nooutput
dx = STATS_min/2.
v1 = NaN
stats $Temp u (v0=v1,v1=$1,dv=v1-v0) index 1 nooutput
dy = STATS_min/2.

set palette rgb 33,13,10
set size ratio -1
set style fill solid 1.0 noborder
set key noautotitle

plot $Data u 1:2:(dx):(dy):3 w boxxy palette
### end of script

Result: