Vectors, fields & coordinates

Each block is the whole file — copy it into x.manic and run manic x.manic (live) or --record out (video).

vector_field

A magnitude-coloured vector field.

// Vector Field — a grid of arrows sampling a named field, coloured by
// magnitude (cyan → lime → magenta), à la Manim's ArrowVectorField.
//
//   manic examples/vector_field.manic
//   manic examples/vector_field.manic --record out --fps 60
//
// Named fields: radial, sink, swirl, saddle, wave, shear, uniform, spiral.

title("Vector Field");
canvas(1280, 720);

text(head, (640, 118), "");  display(head);  color(head, cyan);  size(head, 34);  hidden(head);
text(cap, (640, 668), "");   color(cap, dim);  size(cap, 22);

// two fields, revealed in turn
arrowfield(swirl, (640, 384), 520, 250, swirl, 15);
untraced(swirl);
arrowfield(rad, (640, 384), 520, 250, radial, 15);
untraced(rad);  hidden(rad);

show(head, 0.4);
say(head, "swirl");
say(cap, "a rotational field: (-y, x)");
draw(swirl, 1.2);
wait(1.0);

section("Radial");
say(head, "radial");
say(cap, "an outward source: (x, y) — arrows grow with distance");
par { fade(swirl, 0.5);  show(rad, 0.01); }
draw(rad, 1.2);
wait(1.2);

coordinates

Axes, planes, number lines, polar & complex planes.

// Coordinate Systems — a guided tour of manic's four coordinate frames:
// Axes (ticks + labels), NumberPlane, PolarPlane, and ComplexPlane. Each frame
// fades in, holds, then clears before the next — one centre, four lenses.
//
//   manic examples/coordinates.manic
//   manic examples/coordinates.manic --record out --fps 60

title("Coordinate Systems");
canvas(1280, 720);

text(head, (640, 120), "four ways to draw a plane");
display(head);  color(head, cyan);  size(head, 28);  hidden(head);
text(cap, (640, 640), "");  color(cap, dim);  size(cap, 24);

// --- the four systems, all centred; each starts hidden ---
axes(ax, (640, 384), 540, 210, 45);          // + tick marks and integer labels
plot(wave, (640, 384), 45, 45, sin, 7);       // y = sin(x) drawn on the axes
color(wave, magenta);  untraced(wave);  hidden(ax);

plane(pl, (640, 384), 560, 230, 56);   hidden(pl);
polarplane(pp, (640, 384), 230, 5, 16);   hidden(pp);
complexplane(cp, (640, 384), 560, 230, 56);   hidden(cp);

// --- 1. Axes ---
show(head, 0.5);
section("Axes");
say(cap, "a numbered cross — tick marks every unit");
show(ax, 0.7);
say(cap, "plot y = sin(x) on it");
draw(wave, 1.1);
wait(0.9);
par { fade(ax, 0.4);  fade(wave, 0.4); }

// --- 2. NumberPlane ---
section("Number Plane");
say(cap, "a full cartesian grid");
show(pl, 0.7);
wait(1.0);
fade(pl, 0.4);

// --- 3. PolarPlane ---
section("Polar Plane");
say(cap, "concentric rings and radial spokes — angle and radius");
show(pp, 0.7);
wait(1.0);
fade(pp, 0.4);

// --- 4. ComplexPlane ---
section("Complex Plane");
say(cap, "the same grid, read as real and imaginary parts");
show(cp, 0.7);
wait(1.4);

pie

A pie chart built from sectors.

// Equal Slices — a circle cut into equal *sectors* (real filled pieces, not
// just lines) with the math-kit `pie(id, center, r, n)` builtin. Each slice is
// addressable as p0 … p5, so we can trace them on, then pull two out.
//
//   manic examples/pie.manic
//   manic examples/pie.manic --record out --fps 60

title("Equal Slices");
canvas(1280, 720);

// six equal sectors centred at (560, 400), radius 230 → p0 … p5, tag `p`
pie(p, (560, 400), 230, 6);
untraced(p0);  untraced(p1);  untraced(p2);
untraced(p3);  untraced(p4);  untraced(p5);

text(head, (560, 120), "six equal slices");
display(head);  color(head, cyan);  size(head, 38);  hidden(head);
text(cap, (560, 690), "");  color(cap, dim);  size(cap, 22);

// --- cut the circle equally, one slice at a time ---
show(head, 0.5);
say(cap, "cut the circle into six equal sectors");
stagger(0.12) {
  draw(p0, 0.4);
  draw(p1, 0.4);
  draw(p2, 0.4);
  draw(p3, 0.4);
  draw(p4, 0.4);
  draw(p5, 0.4);
}
wait(0.6);

// --- each sector is a real piece: pull two out and recolour them ---
say(cap, "each sector is a real piece — pull two out");
par {
  move(p0, (621, 435), 0.6, overshoot);
  move(p3, (499, 365), 0.6, overshoot);
  recolor(p0, magenta, 0.5);
  recolor(p3, lime, 0.5);
}
wait(1.0);