Eric, thanks for your suggestions.
I have some explanation about the code examples and my goal.
The large evaluation of RandomReal simulates a chunk of somewhat complicated calculations
involving a large array of vectors on a triangular lattice without showing too much details
but ends up using a similar total time O(1 sec) per cycle when combined with the Map step.
The 10,000 instances of Spheres in the first example also simulates the large Graphics3D object
made up of many 3d Arrows used to display the intermediate status of the vector arrays.
I wanted to check each and every single cycle result real time on screen as the calculation goes on,
but as shown in the first example, many cycles (i=1,2,...,19) are skipped totally,
unlike the much lighter second example which shows the whole progression without skipping.
If I insert Pause at the end of the For execution part as shown in the code example below,
it shows only i=20 when Pause[0] is used (on my computer),
shows i=5,7,9,11,13,15,17,19,20 when Pause[1] is used,
shows i=2,3,4,5,6,7,8,...,19,20 when Pause[2] is used.
Dynamic[a]
For[i = 1, i <= 20, i++, b = RandomReal[{-1, 1}, {50000, 3}];
TextStr = {Text["i=" <> ToString[i], {0, 0, 5}]};
b3g = Map[Sphere[#, 1] &, b];
a = Graphics3D[{TextStr, b3g},
PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}];
Pause[0.2];
]
My guess is that the Graphics3D object of each cycle is thrown at the graphics handler of Mathematica responsible for Dynamic at a pace too fast for it to process and spit out to the screen in time before it receives the next Graphics3D object due to the sheer number of 3D Arrows contained in it.
All I need is that, without using Pause and tuning its time atgument to match the speed of the graphics handler, simply do the calculation and the visualization one after the other as if they are performed by a single computing thread.