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Two dimensional plots

Most examples were adapted from the official pages of Wolfram Language Documentation Center.

The algorithms and implementations of those functions are the intellectual property of Wolfram Research. WLJS Team only reimplemented underlying low-level primitives such as `Line`, `Point`, `Polygon`, and etc.

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Contour Plot​

Generates a contour plot of ff as a function of {x,y}\{x,y\}

ContourPlot[
  Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}
]
(*VB[*)(FrontEndRef["3ca14ac3-7fc1-4e11-bc46-cfa949189d58"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKGycnGpokJhvrmqclG+qapBoa6iYlm5jpJqclWppYGlpYpphaAACMehXU"*)(*]VB*)

Or plot contour lines for which the equation is satisfied

ContourPlot[(*SpB[*)Power[x(*|*),(*|*)2](*]SpB*) - (*SpB[*)Power[y(*|*),(*|*)2](*]SpB*) == (*SpB[*)Power[x(*|*),(*|*)3](*]SpB*), {x, -2, 2}, {y, -2, 2}]
(*VB[*)(FrontEndRef["17562242-ec14-4f0d-a6e4-2105f8af166b"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKG5qbmhkZmRjppiYbmuiapBmk6CaapZroGhkamKZZJKYZmpklAQB1eRU3"*)(*]VB*)

List-version​

ListContourPlot[Table[Sin[i + (*SpB[*)Power[j(*|*),(*|*)2](*]SpB*)], {i, 0, 3, 0.2}, {j, 0, 3, 0.2}], ColorFunction -> "SunsetColors"]
(*VB[*)(FrontEndRef["66d6804b-487e-4ea1-84c2-4b7e451a2aa6"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKm5mlmFkYmCTpmliYp+qapCYa6lqYJBvpmiSZp5qYGiYaJSaaAQB8vBVy"*)(*]VB*)

Density Plot​

Make a simple styled density plot with a custom color function

CoolColor[ z_ ] := RGBColor[z, 1 - z, 1];

DensityPlot[Sin[x y], {x, -1, 1}, {y, -1, 1}, 
 ColorFunction -> CoolColor]
(*VB[*)(FrontEndRef["b6e46278-d904-447a-9d21-81f85788ca58"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJ5mlmpgZmVvoplgamOiamJgn6lqmGBnqWhimWZiaW1gkJ5paAAB44xUA"*)(*]VB*)

Parameteric plots​

Generate a complex paramteric plot

ParametricPlot[
 With[{z = u + I v}, {Re[z + 1/z], Im[z + 1/z]}], {u, -1/2, 
  1/2}, {v, -1/2, 1/2}, PlotRange -> 5, Mesh -> Automatic]
(*VB[*)(FrontEndRef["c73190c7-fdc4-4bad-b90c-b9a6ed5a1607"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJ5sbG1oaJJvrpqUkm+iaJCWm6CYB+UAi0Sw1xTTR0MzAHACO+xYt"*)(*]VB*)

Or a simple mesh

ParametricPlot[{r Cos[\[Theta]], r Sin[\[Theta]]}, {r, 1, 
  2}, {\[Theta], 0, 2 Pi/3}, PlotRange -> All, Mesh -> 15]
(*VB[*)(FrontEndRef["bd006532-1082-422b-864c-4175521dfd27"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJ6UYGJiZGhvpGhpYGOmaGBkl6VqYmSTrmhiam5oaGaakpRiZAwBvDRSj"*)(*]VB*)

Map a texture to it

texture = Image[CellularAutomaton[30, {{1}, 0}, 40], "Bit", Magnification -> 2] // Texture
Texture[(*VB[*)(FrontEndRef["0e7bf45a-331d-4b95-8c8f-a4577e704c95"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKG6SaJ6WZmCbqGhsbpuiaJFma6lokW6TpJpqYmpunmhuYJFuaAgCF6RWC"*)(*]VB*)]
ParametricPlot[{r Cos[\[Theta]], r Sin[\[Theta]]}, {r, 1, 
  2}, {\[Theta], 0, 2 Pi/3}, PlotRange -> All, Mesh -> 15, PlotStyle->texture]
(*VB[*)(FrontEndRef["452e93d0-9815-4671-9d02-202f0a70d567"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKm5gapVoapxjoWloYmuqamJkb6lqmGBjpGhkYpRkkmhukmJqZAwBuXBSD"*)(*]VB*)

Complex Plot​

Plot directly complex space

ComplexPlot[(*FB[*)(((*SpB[*)Power[z(*|*),(*|*)2](*]SpB*) + 1)(*,*)/(*,*)((*SpB[*)Power[z(*|*),(*|*)2](*]SpB*) - 1))(*]FB*), {z, -2 - 2 I, 2 + 2 I}, 
 PlotLegends -> Automatic]
(*VB[*)(Legended[ToExpression[FrontEndRef["a98903f9-675e-4816-95b3-20ef976fe4b6"], InputForm], BarLegend[{ColorDataFunction["MidShiftBalancedHue", "ThemeGradients", {0, 1}, Blend["MidShiftBalancedHue", #1] & ][#1] & , {0, 1}}, LabelStyle -> {}, LegendLayout -> "Column", LegendMarkerSize -> 225, "ColorFunctionShading" -> None, OpacityFunction -> (1 - Rescale[#1, {0, 0.9}, {0, 1}] & ), "OpacityFunctionTicks" -> {{0, "0"}, {0.9, 4}, {1, "Infinity"}}, "OpacityFunctionSize" -> Scaled[0.5], "OpacityFunctionRange" -> {0, 1}, Charting`TickLabels -> {"-\[Pi]", "-\[Pi]/2", "0", "\[Pi]/2", "\[Pi]"}, Ticks -> {{0., 0.25, 0.5, 0.75, 1.}, {{0, 1/20, 1/10, 3/20, 1/5}, {1/5, 1/4, 3/10, 7/20, 2/5}, {2/5, 9/20, 1/2, 11/20, 3/5}, {3/5, 13/20, 7/10, 3/4, 4/5}, {4/5, 17/20, 9/10, 19/20, 1}}}, Charting`TickSide -> Right, ColorFunctionScaling -> True]])(*,*)(*"1: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"*)(*]VB*)

Vector plot​

Generates a vector plot of the vector field {vx,vy}\{v_x, v_y\} as a function of xx and yy

VectorPlot[{x + y, y - x}, {x, -3, 3}, {y, -3, 3}]
(*VB[*)(FrontEndRef["b2aba512-0055-48c1-97ea-e86c8e1cd1f7"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJxklJiWaGhrpGhiYmuqaWCQb6lqapybqplqYJVukGianGKaZAwCDMBXM"*)(*]VB*)

A list version is also available

ListVectorPlot[Table[{y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]]
(*VB[*)(FrontEndRef["ea79add5-017c-4067-b533-e9d2948cb89f"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKpyaaWyampJjqGhiaJ+uaGJiZ6yaZGhvrplqmGFmaWCQnWVimAQCIEhW1"*)(*]VB*)

Stream plot​

Generates a stream plot of the vector field

StreamPlot[{-1 - (*SpB[*)Power[x(*|*),(*|*)2](*]SpB*) + y, 1 + x - (*SpB[*)Power[y(*|*),(*|*)2](*]SpB*)}, {x, -3, 3}, {y, -3, 3}, StreamScale->Large]
(*VB[*)(FrontEndRef["577c61e9-d69f-49d5-a5a1-78f83fb6026f"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKm5qbJ5sZplrqpphZpumaWKaY6iaaJhrqmlukWRinJZkZGJmlAQCBrxWR"*)(*]VB*)

Matrixes & Arrays​

Plots a 2D array or matrix

MatrixPlot[
 Fourier[Table[
   UnitStep[i, 4 - i] UnitStep[j, 7 - j], {i, -7, 7}, {j, -7, 
    7}]]]
(*VB[*)(FrontEndRef["2d01cdec-03d8-4922-a901-1ed71e1ea2c1"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKG6UYGCanpCbrGhinWOiaWBoZ6SZaGhjqGqammBumGqYmGiUbAgCGExW4"*)(*]VB*)

Another example

MatrixPlot[PauliMatrix[3]]
(*VB[*)(FrontEndRef["490bad61-47c1-46f0-b359-853531993ed7"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKm1gaJCWmmBnqmpgnAwmzNAPdJGNTS10LU2NTY0NLS+PUFHMAebIU7g=="*)(*]VB*)

Array plot​

Generates a plot, where values are shown in a discrete array of blocks

ArrayPlot[{{1, 0, 0, Pink}, {1, 1, 0, Pink}, {1, 0, 1, Red}}]
(*VB[*)(FrontEndRef["d40c935a-36b0-4e55-afd9-4033c89cc91c"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKp5gYJFsamybqGpslGeiapJqa6iampVjqmhgYGydbWCYnWxomAwCCMxWj"*)(*]VB*)

Overlay with other graphics

Graphics[{{Red, Disk[{5, 5}, 4]}, 
  Raster[Table[{x, y, x, y}, {x, .1, 1, .1}, {y, .1, 1, .1}]]}]
(*VB[*)(FrontEndRef["8b8dd21a-0df0-4d62-80da-854a15de053b"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKWyRZpKQYGSbqGqSkGeiapJgZ6VoYpCTqWpiaJBqapqQamBonAQCJhBXD"*)(*]VB*)
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