Transforms & morphing
Each block is the whole file — copy it into x.manic and run manic x.manic (live) or --record out (video).
motion-graphics-v2
The generic Motion Graphics V2 acceptance scene: one persistent marker carries an attached
label along a path, becomes a declared visual blueprint, releases the label, gathers the
same particles into a ring, and turns the whole arrangement around one shared pivot. Uses
attach, become, and turn with no renderer flags or subject-specific vocabulary.
// motion-graphics-v2.manic — relationships, identity, and a deliberate settle
title("Motion Graphics V2 — Follow, Become, Turn");
canvas("9:16");
template("mono");
watermark(manicMark, (150, 132), "Made With Manic");
creator(me, "@anish2good name=Manic_Motion tagline=Describe_the_relationship yt=zarigatongy x=@anish2good web=8gwifi.org/manic accent=cyan secondary=magenta footer=social cta=Create_yours safe=reels");
socials(me);
text(kicker, (540, 155), "MOTION GRAPHICS V2");
size(kicker, 23); color(kicker, dim); bold(kicker);
text(headline, (540, 228), "Move the idea, not every coordinate");
size(headline, 40); bold(headline);
text(subhead, (540, 292), "attach · become · turn");
size(subhead, 25); color(subhead, dim);
rect(stage, (540, 865), 900, 1020);
color(stage, panel); outline(stage, dim); opacity(stage, 0.78);
// One authored route and one persistent object.
plot(route, (205, 1040), 172, 190, "0.55*sin(1.2*x)+0.18*x", (0, 4.25));
color(route, cyan); stroke(route, 6); untraced(route);
dot(marker, (205, 1040), 12);
color(marker, gold); glow(marker, 1.6);
text(markerLabel, (205, 994), "one persistent object");
size(markerLabel, 24); color(markerLabel, fg); hidden(markerLabel);
// A hidden target is a visual blueprint; it never appears as a second object.
circle(nodeBlueprint, (935, 885), 56);
color(nodeBlueprint, magenta); outlined(nodeBlueprint); stroke(nodeBlueprint, 7);
glow(nodeBlueprint, 1.2); hidden(nodeBlueprint);
// Supporting particles begin offstage, then arrive as an ordered ring.
rect(seedBox, (540, 610), 260, 180); hidden(seedBox);
particles(sparks, seedBox, 14, 7, 42, "random");
color(sparks, cyan); hidden(sparks);
circle(finalOrbit, (935, 885), 138); hidden(finalOrbit);
text(explain, (540, 1325), "The label follows because the relationship is authored.");
size(explain, 26); color(explain, dim); wrap(explain, 800); hidden(explain);
step("attach-and-travel") {
seq {
attach(markerLabel, marker, (0,-46));
par {
show(markerLabel, 0.35);
show(explain, 0.40);
draw(route, 2.8, smooth);
travel(marker, route, 2.8, smooth);
}
wait(0.45);
}
}
step("become-the-next-idea") {
seq {
par {
become(marker, nodeBlueprint, 1.05, smooth);
say(markerLabel, "same id · new visual state", 0.45);
say(explain, "become preserves identity and settles on the exact blueprint.", 0.45);
}
wait(0.50);
}
}
step("release-arrange-turn") {
seq {
attach(markerLabel, none);
par {
fade(markerLabel, 0.35);
fade(route, 0.45);
show(sparks, 0.30);
arrange(sparks, finalOrbit, "ring", 1.15, smooth);
say(explain, "Release the label. Arrange a system. Turn it around one pivot.", 0.45);
}
turn(sparks, marker, 24, 0.65, out);
wait(1.40);
}
}
motion-graphics-v2-story
The advanced composition example: one question travels through a field of facts, its WHY?
label follows, notation rewrites into a pattern, the question becomes a model, and the same
facts arrange and turn as one knowledge system. Combines attach, become, and turn with
to, travel, flow, spin, arrange, wander, rewrite, seq, par, and stagger.
// motion-graphics-v2-story.manic — one idea, one continuous motion story
title("The Journey of an Idea — Motion Graphics V2 Story");
canvas("9:16");
template("mono");
watermark(manicMark, (170, 178), "Made With Manic");
creator(me, "@anish2good name=Manic_Motion tagline=Move_the_idea yt=zarigatongy x=@anish2good web=8gwifi.org/manic accent=cyan secondary=magenta footer=social cta=Create_yours safe=reels");
socials(me);
// ---------------------------------------------------------------------------
// ONE PERSISTENT STAGE
// The scene never cuts away. Each act reuses what the previous act established.
// ---------------------------------------------------------------------------
text(kicker, (540, 184), "A MOTION GRAPHICS STORY");
size(kicker, 22); color(kicker, dim); bold(kicker); hidden(kicker);
text(headline, (540, 248), "How an idea learns to move");
size(headline, 42); bold(headline); hidden(headline);
text(chapter, (540, 316), "ACT 1 · FOLLOW ATTENTION");
size(chapter, 24); color(chapter, cyan); bold(chapter); hidden(chapter);
rect(stage, (540, 850), 900, 990);
color(stage, panel); outline(stage, dim); opacity(stage, 0.76);
text(narration, (540, 1400), "A question appears before the answer does.");
size(narration, 28); color(narration, fg); wrap(narration, 820); hidden(narration);
text(principle, (540, 1495), "Motion should guide the eye, preserve meaning, then settle.");
size(principle, 22); color(principle, dim); wrap(principle, 820); hidden(principle);
// ---------------------------------------------------------------------------
// ACT 1 — CURIOSITY TRAVELS; ITS CONTEXT FOLLOWS
// ---------------------------------------------------------------------------
spline(questionPath, (175, 1080), (290, 980), (385, 1060), (490, 900), (540, 790));
color(questionPath, cyan); stroke(questionPath, 5); dashed(questionPath, 18, 15);
glow(questionPath, 0.8); untraced(questionPath);
dot(idea, (175, 1080), 12);
color(idea, gold); glow(idea, 1.7); hidden(idea);
text(focusLabel, (175, 1024), "WHY?");
size(focusLabel, 29); color(focusLabel, gold); bold(focusLabel); hidden(focusLabel);
// Facts begin as visual noise. They persist through every later arrangement.
rect(noiseField, (540, 820), 690, 470); hidden(noiseField);
particles(facts, noiseField, 16, 7, 29, "random");
color(facts, cyan); glow(facts, 0.9); hidden(facts);
for i in 0..16 {
tag(facts.p{i}, knowledgeSystem);
}
// ---------------------------------------------------------------------------
// ACT 2 — THE SAME QUESTION BECOMES A MODEL
// ---------------------------------------------------------------------------
equation(work, (540, 1195), `1+2+\cdots+n=?`, 43);
color(work, fg); hidden(work);
// Hidden entities are visual blueprints. `idea` adopts this exact final state.
rect(modelBlueprint, (540, 790), 116, 116);
outlined(modelBlueprint); outline(modelBlueprint, magenta); stroke(modelBlueprint, 7);
rot(modelBlueprint, 45); glow(modelBlueprint, 1.5); hidden(modelBlueprint);
circle(knowledgeOrbit, (540, 790), 250); hidden(knowledgeOrbit);
text(observe, (540, 492), "OBSERVE");
text(connect, (842, 790), "CONNECT");
text(testIdea, (540, 1088), "TEST");
text(explain, (238, 790), "EXPLAIN");
size(observe, 20); size(connect, 20); size(testIdea, 20); size(explain, 20);
color(observe, dim); color(connect, dim); color(testIdea, dim); color(explain, dim);
bold(observe); bold(connect); bold(testIdea); bold(explain);
hidden(observe); hidden(connect); hidden(testIdea); hidden(explain);
tag(observe, knowledgeSystem); tag(connect, knowledgeSystem);
tag(testIdea, knowledgeSystem); tag(explain, knowledgeSystem);
// ---------------------------------------------------------------------------
// ACT 3 — THE MODEL BECOMES A COORDINATED SYSTEM
// ---------------------------------------------------------------------------
text(systemLabel, (540, 648), "ONE IDEA · MANY RELATIONSHIPS");
size(systemLabel, 22); color(systemLabel, magenta); bold(systemLabel); hidden(systemLabel);
text(finalLine, (540, 1320), "Don't animate layers. Animate the relationship.");
size(finalLine, 30); color(finalLine, fg); bold(finalLine); wrap(finalLine, 820); hidden(finalLine);
// ---------------------------------------------------------------------------
// TIMELINE — seq tells the story; par and stagger control the viewing rhythm.
// ---------------------------------------------------------------------------
step("a-question-pulls-attention") {
seq {
par {
show(kicker, 0.35);
show(headline, 0.55);
show(chapter, 0.40);
show(narration, 0.45);
show(principle, 0.45);
show(idea, 0.30);
}
// Stagger turns a cloud into a readable arrival instead of one visual shock.
stagger(0.035) {
for i in 0..16 {
show(facts.p{i}, 0.22);
}
}
attach(focusLabel, idea, (0,-56));
par {
show(focusLabel, 0.30);
draw(questionPath, 2.65, smooth);
travel(idea, questionPath, 2.65, smooth);
flow(questionPath, 1.45);
wander(facts, 2.65);
}
par {
to(idea, scale, 1.55, 0.45, out);
say(narration, "Attention follows the question while the background stays alive.", 0.45);
}
wait(0.55);
}
}
step("the-question-becomes-a-model") {
seq {
attach(focusLabel, none);
par {
fade(focusLabel, 0.30);
fade(questionPath, 0.45);
say(chapter, "ACT 2 · PRESERVE THE IDEA", 0.35);
say(narration, "The question changes form, but it never loses its identity.", 0.45);
show(work, 0.40);
}
// Existing notation moves only where the mathematical meaning changes.
rewrite(work, `1+2+\cdots+n=\frac{n(n+1)}{2}`, 1.00, smooth);
par {
become(idea, modelBlueprint, 1.05, smooth);
arrange(facts, knowledgeOrbit, "ring", 1.20, smooth);
say(principle, "become keeps one id · arrange keeps every particle", 0.45);
}
// spin is local: the new model turns around its own centre.
spin(idea, 90, 0.65, out);
stagger(0.10) {
show(observe, 0.30);
show(connect, 0.30);
show(testIdea, 0.30);
show(explain, 0.30);
}
wait(0.55);
}
}
step("relationships-move-as-one") {
seq {
attach(systemLabel, idea, (0,-142));
par {
show(systemLabel, 0.35);
say(chapter, "ACT 3 · MOVE THE SYSTEM", 0.35);
say(narration, "Now every part can move together without losing the structure.", 0.45);
show(finalLine, 0.45);
}
// turn is relational: particles and labels share one pivot and one motion.
par {
turn(knowledgeSystem, idea, 45, 1.20, smooth);
spin(idea, -135, 1.20, smooth);
to(facts, color, lime, 1.20, smooth);
rewrite(work, `\text{question}\;\longrightarrow\;\text{model}\;\longrightarrow\;\text{insight}`, 1.20, smooth);
}
par {
pulse(idea, 0.70);
say(principle, "FOLLOW · TRANSFORM · COORDINATE · SETTLE", 0.45);
}
wait(1.80);
}
}
reactive-math-journey
A playful vertical journey from 1+1 in Class 1 through fractions, algebra,
geometry, calculus, linear algebra, probability and Fourier analysis to a PhD-level
functional integral — then back to the curiosity that started it all.
// ============================================================================
// reactive-math-journey.manic — from Class 1 counting to PhD curiosity
// ----------------------------------------------------------------------------
// One equation id grows with the learner. `rewrite` keeps the journey continuous
// while a progress marker climbs through school, university and research.
// The ending returns to 1+1: advanced mathematics keeps the original curiosity.
// ============================================================================
title("From 1 + 1 to a PhD in Mathematics");
canvas("9:16");
template("shorts");
watermark(manicMark, (w*0.895-100, h*0.075+24), "Made With Manic");
creator(me, "@anish2good name=Math_Journey tagline=Stay_curious yt=zarigatongy x=@anish2good web=8gwifi.org/manic accent=cyan secondary=magenta footer=social cta=Keep_learning safe=reels");
socials(me);
text(kicker, (540, 135), "THE JOURNEY OF MATHEMATICS");
size(kicker, 23); color(kicker, dim); bold(kicker); hidden(kicker);
text(headline, (540, 225), "From 1 + 1 to a PhD");
size(headline, 47); color(headline, fg); bold(headline); hidden(headline);
text(subhead, (540, 292), "Same curiosity. Bigger questions.");
size(subhead, 25); color(subhead, cyan); bold(subhead); hidden(subhead);
// The learning stage leaves a slim left lane for the climbing progress marker.
rect(stage, (610, 790), 820, 760);
color(stage, panel); outline(stage, dim); opacity(stage, 0.78);
line(rail, (135, 1135), (135, 535));
color(rail, cyan); stroke(rail, 3); dashed(rail, 13, 10); opacity(rail, 0.35);
untraced(rail);
for i in 0..13 {
dot(milestone{i}, (135, 1135 - i*50), 5);
color(milestone{i}, dim); opacity(milestone{i}, 0.55);
}
dot(learner, (135, 1135), 12);
color(learner, cyan); glow(learner, 2.2); hidden(learner);
text(level, (610, 495), "CLASS 1 · COUNTING");
size(level, 25); color(level, cyan); bold(level); hidden(level);
equation(work, (610, 775), `1+1=2`, 58);
hidden(work);
text(note, (610, 1035), "Two apples. One idea. A lifetime of questions begins.");
size(note, 27); color(note, dim); wrap(note, 700); hidden(note);
text(altitude, (540, 1265), "SCHOOL → UNIVERSITY → RESEARCH");
size(altitude, 22); color(altitude, dim); bold(altitude); hidden(altitude);
// ---------------------------------------------------------------------------
// TIMELINE
// ---------------------------------------------------------------------------
par {
show(kicker, 0.40); show(headline, 0.55); show(subhead, 0.55);
show(level, 0.45); show(note, 0.45); show(altitude, 0.45);
draw(rail, 0.90); show(learner, 0.45);
}
show(work, 0.55);
wait(0.85);
// Class 2 — repeated addition discovers multiplication.
par {
say(level, "CLASS 2 · MULTIPLICATION", 0.35);
say(note, "Addition gets impatient and invents a shortcut.", 0.35);
move(learner, (135, 1085), 0.45, smooth);
}
rewrite(work, `3+3+3+3=12`, 0.80, smooth);
wait(0.35);
rewrite(work, `4\times3=\textcolor{lime}{12}`, 0.80, smooth);
wait(0.65);
// Class 5 — pieces become numbers too.
par {
say(level, "CLASS 5 · FRACTIONS", 0.35);
say(note, "Now even pieces of a whole can be added exactly.", 0.35);
move(learner, (135, 1035), 0.45, smooth);
}
rewrite(work, `\frac{1}{2}+\frac{1}{3}=\textcolor{lime}{\frac{5}{6}}`, 0.90, smooth);
wait(0.70);
// Class 7 — the mystery number gets a name.
par {
say(level, "CLASS 7 · ALGEBRA", 0.35);
say(note, "A blank box becomes x — and arithmetic starts telling stories.", 0.35);
move(learner, (135, 985), 0.45, smooth);
}
rewrite(work, `x+3=7`, 0.80, smooth);
wait(0.30);
rewrite(work, `x=\textcolor{lime}{4}`, 0.75, smooth);
wait(0.65);
// Class 8 — shapes reveal equations hidden inside them.
par {
say(level, "CLASS 8 · GEOMETRY", 0.35);
say(note, "A right triangle quietly connects three squares.", 0.35);
move(learner, (135, 935), 0.45, smooth);
}
rewrite(work, `a^2+b^2=\textcolor{cyan}{c^2}`, 0.85, smooth);
wait(0.70);
// Class 10 — one formula solves every quadratic.
par {
say(level, "CLASS 10 · QUADRATICS", 0.35);
say(note, "The unknown now has two possible futures.", 0.35);
move(learner, (135, 885), 0.45, smooth);
}
rewrite(work, `ax^2+bx+c=0`, 0.85, smooth);
wait(0.30);
rewrite(work, `x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}`, 1.00, smooth);
wait(0.75);
// Class 11 — circles turn into identities.
par {
say(level, "CLASS 11 · TRIGONOMETRY", 0.35);
say(note, "Sine and cosine travel differently, but always return to one.", 0.35);
move(learner, (135, 835), 0.45, smooth);
}
rewrite(work, `\sin^2\theta+\cos^2\theta=\textcolor{lime}{1}`, 0.90, smooth);
wait(0.70);
// Class 12 — mathematics learns to describe change itself.
par {
say(level, "CLASS 12 · CALCULUS", 0.35);
say(note, "Not just where things are — how fast they are changing.", 0.35);
move(learner, (135, 785), 0.45, smooth);
}
rewrite(work, `\frac{d}{dx}x^n=\textcolor{cyan}{nx^{n-1}}`, 0.95, smooth);
wait(0.75);
// University — numbers become transformations and uncertain beliefs.
par {
say(level, "UNIVERSITY · LINEAR ALGEBRA", 0.35);
say(note, "Some directions do not turn — they only stretch.", 0.35);
move(learner, (135, 735), 0.45, smooth);
}
rewrite(work, `A\vec v=\textcolor{magenta}{\lambda}\vec v`, 0.90, smooth);
wait(0.70);
par {
say(level, "UNIVERSITY · PROBABILITY", 0.35);
say(note, "Evidence arrives, and a belief learns how to update.", 0.35);
move(learner, (135, 685), 0.45, smooth);
}
rewrite(work, `P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}`, 0.95, smooth);
wait(0.75);
// Graduate study — equations evolve, then decompose into waves.
par {
say(level, "GRADUATE · DIFFERENTIAL EQUATIONS", 0.35);
say(note, "A tiny law of change predicts an entire future.", 0.35);
move(learner, (135, 635), 0.45, smooth);
}
rewrite(work, `\frac{dy}{dt}=ky`, 0.85, smooth);
wait(0.30);
rewrite(work, `y(t)=y_0e^{kt}`, 0.85, smooth);
wait(0.70);
par {
say(level, "GRADUATE · FOURIER ANALYSIS", 0.35);
say(note, "A complicated signal turns out to be a choir of simple waves.", 0.35);
move(learner, (135, 585), 0.45, smooth);
}
rewrite(work, `f(x)=\sum_{n=-\infty}^{\infty}c_ne^{inx}`, 0.95, smooth);
wait(0.75);
// PhD — the symbols are advanced; the habit is still “what if?”
par {
say(level, "PhD · THE EDGE OF WHAT WE KNOW", 0.40);
say(note, "The integral now ranges over every possible field configuration.", 0.40);
move(learner, (135, 535), 0.55, overshoot);
}
rewrite(work, `\mathcal{Z}=\int\mathcal{D}\phi\,e^{-S[\phi]}`, 1.05, smooth);
wait(1.00);
// A loopable ending: the notation grew, but the first question never left.
say(level, "THE REAL DEGREE · STAYING CURIOUS", 0.40);
say(note, "After all that mathematics, the best researchers still ask: why?", 0.40);
rewrite(work, `1+1=\textcolor{lime}{2}`, 1.00, smooth);
pulse(learner, 0.65);
wait(1.80);
reactive-math-notation
One Reels-ready stage exercises structured LaTeX across thirteen notation worlds: algebra, calculus, limits, trigonometry, logic, sums/products, physics, chemistry, biology, probability, matrices/vectors, mixed prose/math, and creator notation.
// ============================================================================
// reactive-math-notation.manic — one Reels-ready stage, thirteen notation worlds
// ----------------------------------------------------------------------------
// `rewrite` is deliberately domain-neutral. The same persistent equation moves
// through algebra, calculus, logic, physics, chemistry, biology, probability
// and linear algebra;
// only changed RaTeX parts leave or enter. Mixed prose + inline math uses normal
// `text`, and the last scene proves creator-defined notation needs no new verb.
// ============================================================================
title("Reactive Mathematics — One Language, Every Notation");
canvas("9:16");
template("shorts");
watermark(manicMark, (w*0.895-100, h*0.075+24), "Made With Manic");
creator(me, "@anish2good name=Notation_Lab tagline=Every_symbol_can_move yt=zarigatongy x=@anish2good web=8gwifi.org/manic accent=cyan secondary=magenta footer=social cta=Create_your_own safe=reels");
socials(me);
text(kicker, (540, 145), "ONE EQUATION · THIRTEEN SCIENTIFIC WORLDS");
size(kicker, 23); color(kicker, dim); bold(kicker); hidden(kicker);
text(headline, (540, 235), "If LaTeX can say it, Manic can move it");
size(headline, 39); color(headline, fg); bold(headline); hidden(headline);
rect(stage, (540, 755), 940, 760);
color(stage, panel); outline(stage, dim); opacity(stage, 0.72); hidden(stage);
text(topic, (540, 445), "01 · ALGEBRAIC REARRANGEMENT");
size(topic, 23); color(topic, cyan); bold(topic); hidden(topic);
equation(work, (540, 730), `2(x+3)=14`, 52);
hidden(work);
text(note, (540, 1040), "Keep the structure. Move only the mathematical change.");
size(note, 25); color(note, dim); wrap(note, 800); hidden(note);
// A normal text entity may freely mix prose and several inline formulas.
text(mixed, (540, 735), `Energy $E=mc^2$ uses mass $m$ and light speed $c$.`);
size(mixed, 31); color(mixed, fg); wrap(mixed, 780); hidden(mixed);
text(scope, (540, 1245), "RaTeX accuracy · local motion · one stable layout");
size(scope, 22); color(scope, dim); bold(scope); hidden(scope);
// A subtle dashed construction line also demonstrates that `dashed` belongs
// to Manic itself — plots and all other path-like entities can use it.
line(rule, (215, 1155), (865, 1155));
color(rule, cyan); stroke(rule, 2); dashed(rule, 12, 9); opacity(rule, 0.35);
untraced(rule);
// ---------------------------------------------------------------------------
// TIMELINE — every chapter reuses `work`; nothing is manually repositioned.
// ---------------------------------------------------------------------------
par {
show(kicker, 0.45); show(headline, 0.55); show(stage, 0.50);
show(topic, 0.45); show(note, 0.45); show(scope, 0.45); draw(rule, 0.85);
}
show(work, 0.55);
wait(0.70);
rewrite(work, `2x=8\quad\Rightarrow\quad \textcolor{lime}{x=4}`, 0.85, smooth);
wait(0.75);
say(topic, "02 · INTEGRALS & DERIVATIVES", 0.35);
say(note, "The Fundamental Theorem becomes a change of state, not a scene cut.", 0.35);
rewrite(work, `F(x)=\int_0^x t^2\,dt`, 0.80, smooth);
wait(0.45);
rewrite(work, `F'(x)=\frac{d}{dx}\int_0^x t^2\,dt=\textcolor{cyan}{x^2}`, 0.95, smooth);
wait(0.70);
say(topic, "03 · FRACTIONS, ROOTS, POWERS & LIMITS", 0.35);
say(note, "Nested notation is still one screen-aware equation.", 0.35);
rewrite(work, `x^2+\sqrt{x}+\frac{1}{x}`, 0.80, smooth);
wait(0.40);
rewrite(work, `\lim_{x\to0}\frac{\sqrt{1+x}-1}{x}=\frac{1}{2}`, 0.95, smooth);
wait(0.70);
say(topic, "04 · TRIGONOMETRIC IDENTITIES", 0.35);
say(note, "The unchanged terms stay; only the conclusion arrives.", 0.35);
rewrite(work, `\sin^2\theta+\cos^2\theta`, 0.80, smooth);
wait(0.40);
rewrite(work, `\sin^2\theta+\cos^2\theta=\textcolor{lime}{1}`, 0.85, smooth);
wait(0.70);
say(topic, "05 · SET NOTATION & LOGIC", 0.35);
say(note, "Membership, intersections and propositions share the same engine.", 0.35);
rewrite(work, `x\in A\cap B`, 0.80, smooth);
wait(0.40);
rewrite(work, `(x\in A)\land(x\in B)`, 0.85, smooth);
wait(0.70);
say(topic, "06 · SUMMATIONS & PRODUCTS", 0.35);
say(note, "Large operators retain their limits and baseline alignment.", 0.35);
rewrite(work, `\sum_{k=1}^{n}k`, 0.80, smooth);
wait(0.40);
rewrite(work, `\prod_{k=1}^{n}k=\textcolor{magenta}{n!}`, 0.85, smooth);
wait(0.70);
say(topic, "07 · PHYSICS FORMULAS & UNITS", 0.35);
say(note, "Symbols and dimensional units can live in one exact expression.", 0.35);
rewrite(work, `F=ma`, 0.80, smooth);
wait(0.40);
rewrite(work, `[F]=\mathrm{kg}\cdot\mathrm{m}\cdot\mathrm{s}^{-2}`, 0.90, smooth);
wait(0.70);
say(topic, "08 · CHEMISTRY · BALANCED REACTIONS", 0.35);
say(note, "Keep every molecule; introduce only the coefficients that balance atoms.", 0.35);
rewrite(work, `H_2+O_2\rightarrow H_2O`, 0.80, smooth);
wait(0.40);
rewrite(work, `\textcolor{cyan}{2}H_2+O_2\rightarrow\textcolor{cyan}{2}H_2O`, 0.90, smooth);
wait(0.70);
say(topic, "09 · BIOLOGY · HARDY–WEINBERG", 0.35);
say(note, "A population model grows from allele frequencies into genotype frequencies.", 0.35);
rewrite(work, `p+q=1`, 0.80, smooth);
wait(0.40);
rewrite(work, `p^2+2pq+q^2=\textcolor{lime}{1}`, 0.90, smooth);
wait(0.70);
say(topic, "10 · PROBABILITY EXPRESSIONS", 0.35);
say(note, "Conditioning expands into Bayes' rule without replacing the stage.", 0.35);
rewrite(work, `P(A\mid B)`, 0.80, smooth);
wait(0.40);
rewrite(work, `P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}`, 0.95, smooth);
wait(0.70);
say(topic, "11 · MATRICES & VECTORS", 0.35);
say(note, "Rows, columns, brackets and vector marks remain genuine LaTeX.", 0.35);
rewrite(work, `\vec v=\begin{bmatrix}1\\2\end{bmatrix}`, 0.85, smooth);
wait(0.40);
rewrite(work, `A\vec v=\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}1\\2\end{bmatrix}`, 1.00, smooth);
wait(0.75);
say(topic, "12 · TEXT MIXED WITH MATHEMATICS", 0.35);
say(note, "Ordinary prose can carry multiple inline formulas naturally.", 0.35);
fade(work, 0.35);
show(mixed, 0.55);
wait(1.25);
fade(mixed, 0.35);
say(topic, "13 · YOUR OWN NOTATION", 0.35);
say(note, "Define the meaning in your story; Manic preserves the supported notation.", 0.35);
rewrite(work, `\mathcal{R}_{\star}(x)\equiv x^2+1`, 0.90, smooth);
wait(0.45);
rewrite(work, `\mathcal{R}_{\star}(2)=\textcolor{lime}{5}`, 0.85, smooth);
wait(1.20);
say(topic, "ONE REACTIVE LANGUAGE", 0.40);
say(note, "Math, physics, logic — creators decide what comes next.", 0.40);
pulse(work, 0.70);
wait(1.80);
quadratic-formula-continuity
The quadratic formula by completing the square with one persistent LaTeX equation.
Each authored rewrite retains unchanged symbols, moves reused terms, and introduces
only the new notation — the acceptance benchmark for structured formula motion.
// quadratic-formula-continuity.manic — structured LaTeX rewrite benchmark
//
// The author supplies correct mathematical states. `rewrite` does not solve
// algebra: it keeps equal RaTeX parts alive, moves them to their new roles,
// introduces only new notation, and settles on the exact target formula.
title("The Quadratic Formula by Completing the Square");
canvas("16:9");
template("plain");
watermark(manicMark, (1135, 30), "Made With Manic");
text(kicker, (cx, 72), "COMPLETING THE SQUARE · ONE CONTINUOUS EQUATION");
size(kicker, 18); color(kicker, dim); bold(kicker); hidden(kicker);
text(guide, (cx, 620), "Stable symbols stay. Only the mathematical change moves.");
size(guide, 19); color(guide, dim); hidden(guide);
equation(
work,
(cx, 330),
`\textcolor{orange}{a}x^2+\textcolor{cyan}{b}x+\textcolor{lime}{c}=0`,
48
);
hidden(work);
show(kicker, 0.45);
show(guide, 0.45);
show(work, 0.65);
wait(1.20);
// Divide through by a.
rewrite(
work,
`x^2+\frac{\textcolor{cyan}{b}}{\textcolor{orange}{a}}x+\frac{\textcolor{lime}{c}}{\textcolor{orange}{a}}=0`,
1.00,
smooth
);
wait(1.00);
// Move c/a across the equality.
rewrite(
work,
`x^2+\frac{\textcolor{cyan}{b}}{\textcolor{orange}{a}}x=-\frac{\textcolor{lime}{c}}{\textcolor{orange}{a}}`,
0.95,
smooth
);
wait(0.95);
// Split the middle coefficient into two equal halves.
rewrite(
work,
`x^2+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x=-\frac{\textcolor{lime}{c}}{\textcolor{orange}{a}}`,
1.05,
smooth
);
wait(0.95);
// Add the completing-square term to both sides.
rewrite(
work,
`x^2+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x+\left(\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)^2=\left(\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)^2-\frac{\textcolor{lime}{c}}{\textcolor{orange}{a}}`,
1.10,
smooth
);
wait(1.05);
// Simplify the right side locally.
rewrite(
work,
`x^2+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}x+\left(\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)^2=\frac{\textcolor{cyan}{b}^2-4\textcolor{orange}{a}\textcolor{lime}{c}}{4\textcolor{orange}{a}^2}`,
1.00,
smooth
);
wait(1.00);
// Expose the repeated factor, then contract it into a square.
rewrite(
work,
`x\left(x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\left(x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)=\frac{\textcolor{cyan}{b}^2-4\textcolor{orange}{a}\textcolor{lime}{c}}{4\textcolor{orange}{a}^2}`,
1.05,
smooth
);
wait(0.90);
rewrite(
work,
`\left(x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}\right)^2=\frac{\textcolor{cyan}{b}^2-4\textcolor{orange}{a}\textcolor{lime}{c}}{4\textcolor{orange}{a}^2}`,
0.95,
smooth
);
wait(1.00);
// Take square roots.
rewrite(
work,
`x+\frac{\textcolor{cyan}{b}}{2\textcolor{orange}{a}}=\pm\frac{\sqrt{\textcolor{cyan}{b}^2-4\textcolor{orange}{a}\textcolor{lime}{c}}}{2\textcolor{orange}{a}}`,
1.05,
smooth
);
wait(1.10);
// Isolate x. The fraction moves across; the discriminant remains itself.
rewrite(
work,
`x=\frac{-\textcolor{cyan}{b}\pm\sqrt{\textcolor{cyan}{b}^2-4\textcolor{orange}{a}\textcolor{lime}{c}}}{2\textcolor{orange}{a}}`,
1.10,
smooth
);
pulse(work, 0.65);
wait(2.50);
transforms
Apply a 2x2 matrix (ApplyMatrix) to a group.
// Transforms — the "animate anything" showcase.
// Named verbs (rotate, spin, scale, move) plus the general `to(id, prop, value)`
// escape hatch, composed with par / seq / stagger.
//
// manic examples/transforms.manic
// manic examples/transforms.manic --record out --fps 60 --crt
title("Transforms");
canvas(1280, 720);
// cast
rect(box, (330, 400), 150, 150); outline(box, cyan);
label(box, "rotate");
rect(dia, (650, 400), 140, 140); outline(dia, magenta);
label(dia, "to");
circle(orb, (980, 400), 62); outline(orb, lime);
label(orb, "spin");
dot(p, (150, 620), 12);
text(cap, (640, 662), ""); color(cap, dim); size(cap, 22);
text(head, (640, 120), "animate anything");
display(head); color(head, cyan); size(head, 40); hidden(head);
// script
show(head, 0.5);
section("Named verbs");
say(cap, "rotate to an absolute angle");
rotate(box, 45, 0.7, overshoot);
say(cap, "spin by a relative angle, twice");
seq {
spin(orb, 180, 0.6);
spin(orb, 180, 0.6);
}
wait(0.4);
section("Animate anything");
say(cap, "to(id, property, value) reaches any property");
par {
to(dia, angle, 45, 0.6, smooth);
to(dia, scale, 1.4, 0.6);
to(dia, color, lime, 0.6);
}
wait(0.4);
say(cap, "compose freely with par / seq / stagger");
stagger(0.12) {
to(box, opacity, 0.4, 0.4);
to(dia, opacity, 0.4, 0.4);
to(orb, opacity, 0.4, 0.4);
}
to(p, x, 1130, 1.0, overshoot);
to(p, color, magenta, 0.4);
wait(1.0);
transform_copy
Duplicate an entity, then transform the copy.
// Copy + Winding Morph — two of the Transform family niceties. `copy(c, a)`
// duplicates a shape so the original stays while the copy transforms; `morph`
// with a spin angle winds the blend (Manim's Clockwise / Counterclockwise
// Transform). Left copy morphs clockwise, right copy counter-clockwise.
//
// manic examples/transform_copy.manic
title("Copy + Winding Morph");
canvas("16:9");
text(head, (cx, 96), "a copy morphs while the original stays -- one CW, one CCW");
color(head, cyan); size(head, 23); hidden(head);
// left: original circle (dim) + a cyan copy that morphs into a square, clockwise
circle(o1, (400, 380), 120); color(o1, dim); stroke(o1, 3); hidden(o1);
rect(t1, (400, 380), 220, 220); hidden(t1);
copy(c1, o1); color(c1, cyan); stroke(c1, 5); glow(c1, 1.6); hidden(c1);
morph(c1, t1, 200); // +200 deg = clockwise wind
// right: same idea, counter-clockwise into a triangle-ish (use another square)
circle(o2, (900, 380), 120); color(o2, dim); stroke(o2, 3); hidden(o2);
rect(t2, (900, 380), 220, 220); hidden(t2);
copy(c2, o2); color(c2, magenta); stroke(c2, 5); glow(c2, 1.6); hidden(c2);
morph(c2, t2, -200); // -200 deg = counter-clockwise
// --- script ---
show(head, 0.5);
par { show(o1, 0.4); show(o2, 0.4); show(c1, 0.4); show(c2, 0.4); }
wait(0.5);
section("Morph the copies");
par { to(c1, morph, 1, 1.8, smooth); to(c2, morph, 1, 1.8, smooth); }
wait(0.9);
par { to(c1, morph, 0, 1.8, smooth); to(c2, morph, 0, 1.8, smooth); }
wait(1.2);
morph
A sampled-point shape morph from A to B.
// Shape Morph — a circle's outline blends smoothly into a square's and back
// (Manim's Transform). `morph(a, b)` samples both outlines to the same number
// of points; `to(a, morph, t)` interpolates between them (t = 0 is `a`'s shape,
// 1 is `b`'s).
//
// manic examples/morph.manic
title("Shape Morph");
canvas("16:9");
text(head, (cx, 110), "a circle becomes a square -- and back");
display(head); color(head, cyan); size(head, 26); hidden(head);
circle(sh, (cx, cy), 150); color(sh, cyan); stroke(sh, 5); glow(sh, 1.6); hidden(sh);
rect(target, (cx, cy), 290, 290); hidden(target); // defines the square outline
morph(sh, target); // set sh up to morph into it
// --- script ---
show(head, 0.5);
show(sh, 0.6);
wait(0.5);
section("Morph");
to(sh, morph, 1, 1.6, smooth); // circle -> square
wait(0.7);
to(sh, morph, 0, 1.6, smooth); // square -> circle
wait(0.7);
to(sh, morph, 1, 1.1, overshoot); // and back, with a bounce
wait(1.4);