# Difference in Plot when using Evaluate vs when not using Evaluate

This example comes from the Mathematica documentation for Plot under Basic Examples.

Can someone please explain why these are each plotted as a different color in this case:

Plot[Evaluate[Table[BesselJ[n, x], {n, 4}]], {x, 0, 10}, Filling -> Axis]


But when Evaluate[] is removed, all of them are the same color:

Plot[Table[BesselJ[n, x], {n, 4}], {x, 0, 10}, Filling -> Axis]


I know it must have to do with the order of things being evaluated, but I'm really not sure why it is working like this - can someone please point me in the correct direction?

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Hmm... I'm almost positive I've seen this question asked here before, but I can't seem to find it... –  David Z Feb 14 '12 at 7:26
Yeah, this is very much an FAQ. –  Ｊ. Ｍ. Feb 14 '12 at 7:55

The list structure is not manifest to Plot as it has the attribute HoldAll (to get a function's attributes, either use Attributes[func] or ??func). Hence Plot evaluates the Table functions as one unit and it appears as if there is only one function, not four.

Evaluate will make the list structure manifest and each function will be plotted with a separate style.

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I apologize if this is naive question, but what does "The list structure is not manifest to Plot" mean? –  brown.2179 Dec 30 '13 at 12:23
It means that Plot isn't seeing the argument as a list. A list is treated as one argument not many arguments as Plot has HoldAll attribute . –  Matariki Dec 31 '13 at 22:06

Plot builds style lists based on the apparent structure of the first argument it is given, before evaluation. List is recognized and elements are styled individually, while generic functions like Table are styled as a whole.

You can see this behavior here, where Sequence acts as a "generic head":

Plot[
{1, Sequence[2, 3], 4}, {x, 0, 1},
PlotRange -> {0, 5},
PlotStyle -> Thick
]


On the other hand sub-lists are recognized and styled:

Plot[
{1, {2, 3}, 4}, {x, 0, 1},
PlotRange -> {0, 5},
PlotStyle -> Thick
]


Clever trick to use Sequence[] to constrain a group to have the same color... :) –  Ｊ. Ｍ. Feb 14 '12 at 8:40
Evaluate simply evaluates your expression which you want to plot. This transforms this one object Table[BesselJ[n, x], {n, 4}] your are give as argument into the several functions. If Plot sees several functions, it knows it can use more colors. Without Evaluate, Plot does not know you have several functions. This comes from the fact, that is has the attribute HoldAll: it does not evaluate your arguments. Without evaluation the first time it sees, that there are several numbers coming out of your function is during the plotting. Then it's too late to color it differently and you get only a single colored plot.