How to combine many ContourPlots using Table?

Question

I noticed that I can plot several functions at the same time using Table and Plot, like this:

Plot[Table[Sin[k x], {k, 0, 3}], {x, 0, 4}]

Why doesn't this approach work with ContourPlot? I tried something like this:

ContourPlot[Table[x + y == k, {k, 0, 3}], {x, -4, 4}, {y, -4, 4}]

which unfortunately returns an empty plot.

ContourPlot[ Table[x + y == k, {k, 0, 3}] // Evaluate, {x, -4, 4}, {y, -4, 4}] — cvgmt, Nov 13, 2020 at 9:17

Ulrich Neumann · Accepted Answer · 2020-11-13 09:17:39Z

3

Add Evaluate

ContourPlot[Evaluate[Table[x + y == k, {k, 0, 3}]], {x, -4, 4}, {y, -4, 4}]

answered Nov 13, 2020 at 9:17

Ulrich Neumann

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$\begingroup$ Amazing. Thank you! Could you please elaborate a bit more why we need Evaluate here, or in which cases in general Evaluate is necessary? (in particular, why it's not necessary with Plot) $\endgroup$
– ersbygre1
Nov 13, 2020 at 9:21
$\begingroup$ Probably because Table has attribute Hold All and Evaluate forces evaluation $\endgroup$
– Ulrich Neumann
Nov 13, 2020 at 9:32
$\begingroup$ ...and Plot doesn't care about Hold All? $\endgroup$
– ersbygre1
Nov 13, 2020 at 9:37
2

$\begingroup$ @Stephan - Plot also needs an Evaluate for intended behavior. Compare Plot[Table[Sin[k x], {k, 0, 3}], {x, 0, 4}] with Plot[Table[Sin[k x], {k, 0, 3}] // Evaluate, {x, 0, 4}] $\endgroup$
– Bob Hanlon
Nov 13, 2020 at 12:28
$\begingroup$ I see, thank you! $\endgroup$
– ersbygre1
Nov 14, 2020 at 0:29

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