mathics3`
Graphics[Table[{Hue[h, s], Disk[{12h, 8s}]}, {h, 0, 1, 1/6}, {s, 0, 1, 1/4}]]
`
mathics3`Plot[{Sin[x], Cos[x], x ^ 2}, {x, -1, 1}]`
await visibility(mathics3`
f[x_] := 4 x / (x ^ 2 + 3 x + 5);
{f'[x], f''[x], f'''[x]} // Together
`)
await visibility(mathics3`
f[x_] := 4 x / (x ^ 2 + 3 x + 5);
{f'[x], f''[x], f'''[x]} // Together // FullForm
`)
await visibility(mathics3`
Graphics[Table[{EdgeForm[{GrayLevel[0, 0.5]}], Hue[(-11+q+10r)/72, 1, 1, 0.6], Disk[(8-r){Cos[2Pi q/12], Sin[2Pi q/12]}, (8-r)/3]}, {r, 6}, {q, 12}]]
`)
await visibility(
mathics3`ColorNegate[Import["ExampleData/sunflowers.jpg"]] // MathMLForm`
)
{
await visibility();
return mathics3`DominantColors[Import["ExampleData/hedy.tif"]] // MathMLForm`;
}
await visibility(mathics3`
Graphics[Table[{AbsoluteThickness[t], Line[{{20 t, 10}, {20 t, 80}}], Text[ToString[t]<>"pt", {20 t, 0}]}, {t, 0, 10}]]
`)
await visibility(mathics3`
Table[Graphics[{Circle[], Arrow[Table[{Cos[phi],Sin[phi]},{phi,0,2*Pi,Pi/2}],{d, d}]}],{d,0,2,0.5}] // MathMLForm
`)
await visibility(mathics3`
Table[Style[Graphics[{EdgeForm[{Black}], RGBColor[r,g,b], Rectangle[]}], ImageSizeMultipliers->{0.2, 1}], {r,0,1,1/2}, {g,0,1,1/2}, {b,0,1,1/2}] // TableForm // MathMLForm
`)
await visibility(mathics3`
collatz[1] := 1;
collatz[x_ ? EvenQ] := x / 2;
collatz[x_] := 3 x + 1;
list = FixedPointList[collatz, 14];
ListLinePlot[list]
`)
{
await visibility();
return mathics3`
vertices = {{0,0}, {1,0}, {.5, .5 Sqrt[3]}};
points = NestList[.5(vertices[[ RandomInteger[{1,3}] ]] + #)&, {0.,0.}, 1000];
Graphics[Point[points], ImageSize->Large]
`;
}
await visibility(
mathics3`ListLinePlot[Table[Sin[x], {x, -5, 5, 0.2}], Filling->Axis]`
)
await visibility(
mathics3`DensityPlot[Sin[x y], {x, -2, 2}, {y, -2, 2}, Mesh->Full]`
)
await visibility(mathics3`ParametricPlot[{Sin[u], Cos[3 u]}, {u, 0, 2 Pi}]`)
{
await visibility();
return mathics3`Clear[t]; PolarPlot[{1, 1 + Sin[20 t] / 5}, {t, 0, 2 Pi}]`;
}
await visibility(mathics3`
WordCloud[StringSplit[Import["ExampleData/EinsteinSzilLetter.txt", CharacterEncoding->"UTF8"]]] // MathMLForm
`)
await visibility(
mathics3`EdgeDetect[Import["ExampleData/hedy.tif"], 5] // MathMLForm`
)
await visibility(mathics3`Apart[1 / (x^2 - y^2), x]`)
{
await visibility();
return mathics3`
With[{f = {Cos[x] + Sin[x], Sin[x]}},
Graphics[
Table[{Hue[t/(2 Pi), 1, .8], Line[{f, Normalize[D[f, x]] + f}]} /.
x -> t, {t, 0, 2 Pi, .1}]]]
`;
}
await visibility(mathics3`Integrate[Sin[x] ^ 5, x]`)
await visibility(mathics3`Series[Exp[x-y], {x, 0, 2}, {y, 0, 2}]`)
await visibility(mathics3`
Graphics[
Table[{EdgeForm[Black], Hue[RandomReal[]],
Disk[RandomReal[4, {2}], RandomReal[1]]}, {40}]]
`)
await visibility(mathics3`
Graphics[
Table[{Hue[t/15, 1, .9, .3],
Disk[{Cos[2 Pi t/15], Sin[2 Pi t/15]}]}, {t, 15}]]
`)
await visibility(mathics3`
Graphics[{Red, Disk[{0, 0}, 2, {0, Pi}], Blue,
Disk[{0, 0}, 2, {Pi, 2 Pi}], Red, Disk[{-1, 0}, 1], Blue,
Disk[{1, 0}, 1]}, ImageSize -> 150]
`)
await visibility(mathics3`
Solve[{3 x ^ 2 - 3 y == 0, 3 y ^ 2 - 3 x == 0}, {x, y}] // Simplify
`)
await visibility(mathics3`
Graphics[Line[AnglePath[RandomReal[{-1, 1}, {100}]]]]
`)
await visibility(mathics3`Nest[Subsuperscript[#,#,#]&,0,5]`)
{
await visibility();
return mathics3`
lindenmayer[i_, b_, h_, j_, r_, n_] :=
(a = h; p = j; s = k = {}; t = Flatten;
(Switch[#,
6, s = {a, p, s},
8, {a, p, s} = s,
_C, k = {k, Line@{p, p += {Cos@a, Sin@a}}}];
If[# < 9, a += I^# b ]) & /@ t@Nest[# /. r &, i, n];
Graphics@t@k);
lindenmayer[{C[1], X}, Pi/2, 0, {0, 0}, {X -> {X, 4, Y, C[1]}, Y -> {C[1], X, 2, Y}}, 10]
`;
}
await visibility(
mathics3`ListPlot[Table[ElementData[z, "AtomicWeight"], {z, 118}]]`
)
await visibility(mathics3`
Clear[a]; RSolve[{a[n + 2] == a[n], a[0] == 1, a[1] == 4}, a, n]
`)
function mathics3_graph(strings) {
mathics3`LoadModule["pymathics.graph"]`;
return mathics3(strings);
}
await visibility(mathics3_graph`CompleteGraph@20`)
await visibility(mathics3_graph`BinomialTree[3, DirectedEdges->True]`)
await visibility(mathics3_graph`GraphData["PappusGraph"]`)
await visibility(mathics3`Graphics3D[Sphere[]]`)
async function mathics3(strings) {
const [type, result] = await mathics3_js(strings[0]);
if (type === "code") {
return md`\`\`\`mathematica\n${result}\n\`\`\``;
} else if (type === "math") {
return tex.block`${result}`;
} else if (type === "json") {
return JSON.parse(result);
} else if (type === "html") {
return html`${result}`;
} else {
return result;
}
}
mathics3_js = (query) => py`${mathics3_py}(${query})`
mathics3_py = py`
import micropip
await micropip.install([
"Mathics3",
"https://mathics3.github.io/Mathics3-live/pypi/Mathics3_notebook_frontends-0.1.0-py3-none-any.whl",
"pymathics-graph",
"ipywidgets",
"lxml",
"pyocr",
"scikit-image",
"unidecode",
"wordcloud",
])
from mathics3_kernel.frontend.generic import mathics3
mathics3
`
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
