visualize 4-dimensional data

Data Structure

Values indexed by 3 indices: {{{value(x,y,z)}}}

Data is a collection of data point of form

{x, y, z, value}

Visualization

Color-encode value

Use //Mathematica//'s ListPointPlot3D function

{{{ In[1]:= data=Table[{RandomReal[],RandomReal[],RandomReal[],RandomReal[]},{1000}];

In[2]:= data//RandomSample[#,5]&//TableForm Out[2]//TableForm= 0.908684 0.733667 0.678761 0.13171 0.453014 0.880303 0.190896 0.661927 0.527378 0.698978 0.908703 0.449359 0.449864 0.451687 0.816574 0.763383 0.648244 0.763775 0.326942 0.602782

In[3]:= ListPointPlot3D[ {#}&/@dataAll,1;;3, PlotStyle-> ({Opacity[2*#],PointSize[.01],ColorData["TemperatureMap"][#]}&/@dataAll,4), Filling-> Bottom, FillingStyle-> {Opacity[.04]}, AxesLabel-> {"x","y","z"}, PlotLabel-> "color temperature ~ f(x,y,z)", ImageSize->600 ] }}}

ListPointPlot3DExample.png