Update or Animate an ArrayPlot or MatrixPlot?

Question

I am trying to add new row or column or points to a 2D plot as I keep generating the values. The trick is by using this method I will not be required to store the big array or matrix and will be helpful in plotting suppose $50000\times 4000$ array size. By the end of the loop, I want to the get 2D plot without storing array or matrix. See the example code.

This could be implemented in MATLAB as initializing figure with some size and properties, hold on and adding each row or data point as generated.

a = Table[{0}, {5000}, {6000}]; (* initialize*)

For[k = 1, k <= 5000, k++,

line = 2*k*Range[1,6000]; (* random way of getting data value at (k,t) index*)

(* here write graphics command to add new row points at index (k,t) to the 2D plot*)

]

Answer 1

A possible solution is to not store the data, but rather to store plots of the data at each step. These plots can be combined together using Show, but the data that were used to generate them can be discarded.

xmin = 1;
xmax = 5;
xstep = 1;
plotList = {};

Monitor[
  Do[
    AppendTo[plotList, 
     Plot[x Cos[x], 
         {x, 0 + (i*2 Pi), 2 Pi + (i*2 Pi)}, 
         PlotStyle -> ColorData[i, "ColorList"]]];
    Pause[2];
   , {i, xmin, xmax, xstep}];
 , Show[plotList, PlotRange -> All]
 ]

The final plot (shown here) demonstrates that the different segments were plotted with different colors:

Show[plotList, PlotRange -> All]