How exactly works Evaluate function in Wolfram Mathematica. How does it make a difference in two plots below

I'm trying to understand how exactly works function Evaluate. Here I have two examples and the only difference between them is function Evaluate.

First plot with Evaluate.

ReliefPlot[
 Table[Evaluate[Sum[Sin[RandomReal[9, 2].{x, y}], {20}]], {x, 1, 2, .02}, 
                                                          {y, 1, 2, .02}], 
ColorFunction -> 
(Blend[{Darker[Green, .8], Lighter[Brown, .2],White}, #] &), 
  Frame -> False, Background -> None, PlotLegends -> Automatic]

https://i.sstatic.net/XPOf8.png "plot1"

Second plot without Evaluate.

ReliefPlot[
 Table[Sum[Sin[RandomReal[9, 2].{x, y}], {20}], {x, 1, 2, .02}, 
                                                {y, 1,2, .02}], 
ColorFunction -> 
(Blend[{Darker[Green, .8], Lighter[Brown, .2], White}, #] &),
 Frame -> False, Background -> None, 
 PlotLegends -> Automatic]

https://i.sstatic.net/rdRAB.png "plot2"

Please explain how Evaluate makes a difference here.

Solution

Compare this

count=0;
ReliefPlot[Table[Sum[Sin[count++;RandomReal[9,2].{x,y}],{20}],{x,1,2,.02},{y,1,2,.02}]]
count

which should display your plot followed by 52020=51*51*20 because you have a 51*51 Table and each entry needs to evaluate the 20 iterations of your Sum

with this

count=0;
ReliefPlot[Table[Evaluate[Sum[Sin[count++;RandomReal[9,2].{x,y}],{20}]],{x,1,2,.02},{y,1,2,.02}]]
count

which should display your plot followed by 20 because the Evaluate needed to do the 20 iterations of your Sum only once, even though you do see 51*51 blocks of different colors on the screen.

You will get the same counts displayed, without the graphics, if you remove the ReliefPlot from each of these, so that seems to show it isn't the ReliefPlot that is responsible for the number of times your RandomReal is calculated, it is the Table.

So that Evaluate is translating the external text of your Table entry into an internal form and telling Table that this has already been done and does not need to be repeated for every iteration of the Table.

What you put and see on the screen is the front end of Mathematica. Hidden behind that is the back end where most of the actual calculations are done. The front and back ends communicate with each other during your input, calculations, output and display.

But this still doesn't answer the question why the two plots look so different. I am guessing that when you don't use Evaluate and thus don't mark the result of the Table as being complete and finished then the ReliefPlot will repeatedly probe that expression in your Table and that expression will be different every time because of the RandomReal and this is what displays the smoother higher resolution displayed graphic. But when you do use the Evaluate and thus the Table is marked as done and finished and needs no further evaluation then the ReliefPlot just uses the 51*51 values without recalculating or probing and you get a lower resolution ReliefPlot.

As with almost all of Mathematica, the details of the algorithms used for each of the thousands of different functions are not available. Sometimes the Options and Details tab in the help page for a given function can give you some additional information. Experimentation can sometimes help you guess what is going on behind the code. Sometimes other very bright people have figured out parts of the behavior and posted descriptions. But that is probably all there is.