Manim Composer

Workflow

Phase 1: Understand the Concept

1. Research the topic deeply before asking questions

• Use web search to understand the core concepts
• Identify the key insights that make this topic interesting
• Find the "aha moment" - what makes this click for learners
• Note common misconceptions to address

2. Identify the narrative hook

• What question does this video answer?
• Why should the viewer care?
• What's the surprising or counterintuitive element?

Phase 2: Clarify with User

Ask targeted questions (not all at once - adapt based on responses):

Audience & Scope

• What math/science background should I assume? (e.g., "knows calculus" or "high school algebra")
• Target video length? (short: 5-10min, medium: 15-20min, long: 30min+)
• Should this be self-contained or part of a series?

Focus & Depth

• Any specific aspects to emphasize or skip?
• Proof-heavy or intuition-focused?
• Real-world applications to include?

Style Preferences

• Color scheme preferences?
• Narration style? (casual, formal, playful)
• Any specific visual metaphors you have in mind?

Phase 3: Create scenes.md

Output a comprehensive scenes.md file with this structure:

# [Video Title]

## Overview
- **Topic**: [Core concept]
- **Hook**: [Opening question/mystery]
- **Target Audience**: [Prerequisites]
- **Estimated Length**: [X minutes]
- **Key Insight**: [The "aha moment"]

## Narrative Arc
[2-3 sentences describing the journey from confusion to understanding]

---

## Scene 1: [Scene Name]
**Duration**: ~X seconds
**Purpose**: [What this scene accomplishes]

### Visual Elements
- [List of mobjects needed]
- [Animations to use]
- [Camera movements]

### Content
[Detailed description of what happens, what's shown, what's explained]

### Narration Notes
[Key points to convey, tone, pacing notes]

### Technical Notes
- [Specific Manim classes/methods to use]
- [Any tricky implementations to note]

---

## Scene 2: [Scene Name]
...

---

## Transitions & Flow
[Notes on how scenes connect, recurring visual motifs]

## Color Palette
- Primary: [color] - used for [purpose]
- Secondary: [color] - used for [purpose]
- Accent: [color] - used for [purpose]
- Background: [color]

## Mathematical Content
[List of equations, formulas, or mathematical objects that need to be rendered]

## Implementation Order
[Suggested order for implementing scenes, noting dependencies]

3b1b Style Principles

Apply these principles when composing scenes:

Visual Storytelling

• Show, don't just tell - Every concept needs a visual representation
• Progressive revelation - Build complexity gradually, don't show everything at once
• Visual continuity - Transform objects rather than replacing them when possible

Pacing & Rhythm

• Pause for insight - Give viewers time to absorb key moments
• Vary the pace - Mix quick sequences with slower explanations
• End scenes with resolution - Each scene should feel complete

Mathematical Beauty

• Emphasize elegance - Highlight when math is surprisingly simple or beautiful
• Connect representations - Show the same concept multiple ways (algebraic, geometric, intuitive)
• Embrace abstraction gradually - Start concrete, then generalize

Engagement Techniques

• Pose questions - Make viewers curious before revealing answers
• Acknowledge difficulty - "This might seem confusing at first..."
• Celebrate insight - Make the "aha moment" feel earned

References

• references/narrative-patterns.md - Common 3b1b narrative structures
• references/visual-techniques.md - Effective visualization patterns
• references/scene-examples.md - Example scenes.md excerpts

Templates

• templates/scenes-template.md - Blank scenes.md template

Narrative Patterns for Math Explainers

Common structures used in effective 3Blue1Brown-style videos.

Pattern 1: Mystery → Investigation → Resolution

Structure: 1. Present a puzzling result or paradox 2. Investigate why it's true through visual exploration 3. Reveal the underlying principle 4. Show how the principle generalizes

Example topics: Euler's identity, Bayes theorem, infinite series paradoxes

Opening hooks:

• "What does it even mean to raise a number to an imaginary power?"
• "This equation looks wrong, but it's actually true..."
• "Most people get this probability question wrong..."

---

Pattern 2: Build Up → Payoff

Structure: 1. Introduce simple building blocks 2. Combine them to create something complex 3. Show the beautiful/surprising result 4. Reflect on why it works

Example topics: Fourier series, neural networks, linear algebra

Opening hooks:

• "Let's start with something simple..."
• "Each piece here is easy, but together they do something remarkable..."

---

Pattern 3: Two Perspectives → Unity

Structure: 1. Show concept from perspective A (e.g., algebraic) 2. Show same concept from perspective B (e.g., geometric) 3. Reveal they're the same thing 4. Explore implications of this connection

Example topics: Dot product, determinants, complex multiplication

Opening hooks:

• "There are two ways to think about this..."
• "These seem like completely different ideas, but..."

---

Pattern 4: Wrong → Less Wrong → Right

Structure: 1. Present common misconception or naive approach 2. Show why it fails 3. Refine the approach 4. Arrive at correct understanding

Example topics: Limits, probability distributions, definitions

Opening hooks:

• "Your first instinct here is probably wrong..."
• "The obvious approach doesn't quite work..."

---

Pattern 5: Specific → General

Structure: 1. Solve a specific concrete example 2. Notice patterns in the solution 3. Abstract to general principle 4. Apply to new situations

Example topics: Derivatives, group theory, algorithm analysis

Opening hooks:

• "Let's work through a specific example..."
• "Once you see the pattern here, it shows up everywhere..."

---

Pattern 6: History as Narrative

Structure: 1. Present the problem as historically encountered 2. Follow the journey of discovery 3. Show key insights that led to breakthroughs 4. Connect to modern understanding

Example topics: Calculus, cryptography, quantum mechanics

Opening hooks:

• "Imagine you're a mathematician in the 1600s..."
• "This problem stumped the greatest minds for centuries..."

---

Combining Patterns

Most effective videos combine multiple patterns:

• Mystery hook + Build Up explanation
• Two Perspectives + Specific → General examples
• Wrong → Right + History narrative

Pacing Guidelines

Emotional Arc

Every video should have emotional beats:

1. Curiosity (opening) - Why should I care? 2. Confusion (early) - This is harder than it looks 3. Partial clarity (middle) - I'm starting to see... 4. Aha moment (climax) - Oh! That's beautiful! 5. Satisfaction (end) - Now I truly understand

Scene Examples

Example scene breakdowns from 3b1b-style videos.

---

Example 1: Explaining the Dot Product

Scene 1: The Question

Duration: ~30 seconds Purpose: Hook the viewer with the mystery

Visual Elements

• Two vectors a and b drawn as arrows
• The dot product formula: a · b = |a||b|cos(θ)
• Question mark animation

Content Open on two vectors. Show the formula. Pose the question: "Why does multiplying components and adding them give you something related to the angle between vectors?"

Narration Notes Tone: curious, slightly puzzled. Emphasize that the formula seems arbitrary.

Technical Notes

• Use Arrow for vectors
• MathTex for formula
• Indicate() on the cos(θ) term

---

Scene 2: Geometric Interpretation

Duration: ~90 seconds Purpose: Show projection interpretation

Visual Elements

• Vector a (horizontal, blue)
• Vector b (angled, green)
• Projection of b onto a (dashed line)
• Right angle marker
• Length labels

Content Show that a · b equals |a| times the projection of b onto a. Animate the projection dropping down. Show this equals |a||b|cos(θ) geometrically.

Narration Notes "The dot product measures how much one vector goes in the direction of another."

Technical Notes

• DashedLine for projection
• RightAngle mobject
• animate.rotate() for showing different angles

---

Scene 3: Numeric Connection

Duration: ~60 seconds Purpose: Connect geometry to algebra

Visual Elements

• Coordinate grid
• Vector a = [a₁, a₂]
• Vector b = [b₁, b₂]
• Components highlighted

Content Show vectors on grid with components labeled. Demonstrate why a₁b₁ + a₂b₂ equals the geometric interpretation. Use specific numbers.

Narration Notes Walk through calculation slowly. "Let's see why the algebra matches the geometry."

Technical Notes

• NumberPlane or Axes
• Brace for component labels
• TransformMatchingTex for equation steps

---

Example 2: Introduction to Fourier Series

Scene 1: The Hook

Duration: ~45 seconds Purpose: Show the surprising result

Visual Elements

• A square wave (sharp corners)
• Sum of smooth sine waves
• Morphing animation between them

Content "You can build a square wave—something with sharp corners—from perfectly smooth sine waves." Show the result first, then promise to explain how.

Narration Notes Tone: wonder, slight disbelief. This should feel surprising.

Technical Notes

• ParametricFunction for waves
• Transform animation for the morph
• Consider showing 1, 3, 5 terms building up

---

Scene 2: Building Blocks

Duration: ~120 seconds Purpose: Introduce sine waves as basis

Visual Elements

• Single sine wave
• Frequency visualization (faster oscillation)
• Amplitude visualization (taller/shorter)
• Phase visualization (shifting left/right)

Content Introduce the three parameters: frequency, amplitude, phase. Show each one separately, then combine.

Narration Notes Go slow. "A sine wave has three knobs we can adjust..."

Technical Notes

• ValueTracker for animating parameters
• Updaters to make wave respond to trackers
• Labels for each parameter

---

Scene 3: Superposition

Duration: ~90 seconds Purpose: Show waves can be added

Visual Elements

• Two sine waves (different colors)
• Their sum (third color)
• Point-by-point addition visualization

Content Show that adding waves means adding their heights at each point. Demonstrate with two specific frequencies combining.

Narration Notes "Adding waves is simple—at each point, just add the heights."

Technical Notes

• VGroup of three function graphs
• Vertical lines showing addition at specific x values
• Animate the addition happening

---

Example 3: Matrix as Linear Transformation

Scene 1: Grid Transformation

Duration: ~60 seconds Purpose: Visual foundation

Visual Elements

• 2D coordinate grid (NumberPlane)
• Basis vectors i-hat and j-hat (colored arrows)
• Grid lines transforming

Content Show a grid. Highlight i-hat (1,0) and j-hat (0,1). Apply a transformation—watch the entire grid move while tracking where basis vectors land.

Narration Notes "Watch what happens to the grid when we apply this transformation. Notice how every point moves."

Technical Notes

• NumberPlane with visible grid lines
• apply_matrix() method
• Keep basis vectors visually distinct

---

Scene 2: Basis Vectors Determine Everything

Duration: ~90 seconds Purpose: Key insight

Visual Elements

• Transformed i-hat and j-hat
• Arbitrary vector v as combination
• v = xi + yj visualization

Content Show that knowing where i-hat and j-hat land tells you where ANY vector lands. Because v = xi + yj, the transformed v = x(new i) + y(new j).

Narration Notes "Here's the key insight..." Build anticipation before the reveal.

Technical Notes

• Vector addition animation (tip-to-tail)
• Scaling animation for coefficients
• TransformMatchingShapes for the combination

---

Scene Transition Patterns

Zoom Focus

Full scene → Zoom into detail → Explain → Zoom out

Side-by-Side Build

Empty left | Empty right
Add to left | Compare
Add to right | Connect them

Transform Chain

Object A → Transform → Object B → Transform → Object C
(Maintain visual continuity throughout)

Reset and Rebuild

Complex scene → Clear/fade most → Focus on one element → Build new complexity

Visual Techniques for Math Animation

Effective visualization patterns for explaining mathematical concepts.

Core Principles

1. Progressive Disclosure

Never show everything at once. Build complexity gradually.

Bad: Show complete equation immediately Good: Build equation term by term, explaining each part

Scene flow:
1. Show simple case: f(x) = x²
2. Add complexity: f(x) = ax²
3. Full form: f(x) = ax² + bx + c

2. Transform, Don't Replace

When possible, morph objects into new forms rather than fading out/in.

Bad: FadeOut(equation1), FadeIn(equation2) Good: TransformMatchingTex(equation1, equation2)

This maintains visual continuity and shows the relationship between forms.

3. Color as Meaning

Use color consistently to encode meaning throughout the video.

Pattern:

• Input/given values: BLUE
• Output/results: GREEN
• Key terms being discussed: YELLOW highlight
• Errors/negatives: RED
• Neutral/supporting: WHITE/GREY

4. Spatial Relationships

Position encodes relationships:

• Left-to-right: transformation, time, causation
• Top-to-bottom: hierarchy, derivation
• Center: focus of attention
• Periphery: context, reference

---

Animation Techniques

Highlighting & Focus

Indicate - Brief flash to draw attention

self.play(Indicate(term))

Circumscribe - Circle around important element

self.play(Circumscribe(equation, color=YELLOW))

FlashAround - Dramatic attention on revelation

self.play(FlashAround(result))

Equation Manipulation

Isolate terms - Color or move specific parts

equation.set_color_by_tex("x", BLUE)

Step-by-step derivation - Show each algebraic step

step1 = MathTex(r"2x + 4 = 10")
step2 = MathTex(r"2x = 6")
step3 = MathTex(r"x = 3")
# Transform between steps with alignment

Substitution - Show value being plugged in

# Animate the number moving into the variable's position

Geometric Intuition

Coordinate systems - Always label axes

axes = Axes(x_range=[-3, 3], y_range=[-2, 2])
labels = axes.get_axis_labels(x_label="x", y_label="f(x)")

Trace paths - Show how points move

trace = TracedPath(dot.get_center, stroke_color=YELLOW)

Area visualization - For integrals, sums

area = axes.get_area(graph, x_range=[a, b], color=BLUE, opacity=0.5)

3D Techniques

Camera orbiting - Reveal 3D structure

self.play(frame.animate.reorient(60, 70), run_time=3)

Projection - Show 3D object's 2D shadow

# Helps connect 3D intuition to 2D formulas

Slicing - Cut through 3D objects

# Show cross-sections to understand structure

---

Common Visual Metaphors

Vectors as Arrows

• Position vectors: arrows from origin
• Addition: tip-to-tail
• Scaling: stretching/shrinking

Functions as Machines

• Input goes in one side
• Transformation happens
• Output comes out

Matrices as Transformations

• Show grid being transformed
• Track where basis vectors go
• Emphasize determinant as area scaling

Derivatives as Slopes

• Tangent line touching curve
• Zoom in to show local linearity
• Animate slope changing as point moves

Integrals as Accumulation

• Riemann sums with rectangles
• Width → 0 animation
• Area filling under curve

---

Scene Composition

The Golden Layout

┌─────────────────────────────────┐
│           TITLE/CONTEXT         │  (top edge)
├─────────────────────────────────┤
│                                 │
│      MAIN VISUALIZATION         │  (center, largest area)
│                                 │
├─────────────────────────────────┤
│    EQUATION / FORMULA           │  (bottom third)
└─────────────────────────────────┘

Side-by-Side Comparison

┌───────────────┬───────────────┐
│   BEFORE /    │   AFTER /     │
│   CONCEPT A   │   CONCEPT B   │
└───────────────┴───────────────┘

Zoomed Detail

┌─────────────────────────────────┐
│  ┌─────┐                        │
│  │ZOOM │ ←── magnified detail   │
│  └─────┘                        │
│         Main context            │
└─────────────────────────────────┘

---

Timing Guidelines

Rhythm Pattern

Fast-fast-SLOW-fast-fast-SLOW

Quick animations for setup, slow down for key insights.

---

Color Palettes

Classic 3b1b

• Background: #1C1C1C (dark grey)
• Primary: #58C4DD (blue)
• Secondary: #83C167 (green)
• Accent: #FFFF00 (yellow)
• Warning: #FF6666 (red)

High Contrast

• Background: #000000
• Primary: #FFFFFF
• Accent: #FFD700

Soft Academic

• Background: #2D2D2D
• Primary: #6ECFFF
• Secondary: #98E898
• Accent: #FFE66D

[Video Title]

Overview

• Topic: [Core mathematical/scientific concept]
• Hook: [Opening question or mystery that draws viewers in]
• Target Audience: [Prerequisites - what math/science background is assumed]
• Estimated Length: [X minutes]
• Key Insight: [The central "aha moment" - the one thing viewers should remember]

Narrative Arc

[2-3 sentences describing the emotional and intellectual journey. Example: "We start with a puzzling observation, investigate why it's true, and discover a beautiful underlying principle that connects seemingly different ideas."]

---

Scene 1: [Scene Name]

Duration: ~X seconds Purpose: [What this scene accomplishes in the overall narrative]

Visual Elements

• [Mobject 1: description, color, position]
• [Mobject 2: description, color, position]
• [Animation sequence]
• [Camera movements if any]

Content

[Detailed description of what happens visually and conceptually. Be specific enough that someone could implement this scene.]

Narration Notes

[Key points to convey, suggested tone, pacing. Not a full script, but guidance.]

Technical Notes

• [Specific Manim classes to use]
• [Tricky implementations or gotchas]
• [Dependencies on previous scenes]

---

Scene 2: [Scene Name]

Duration: ~X seconds Purpose: [Purpose]

Visual Elements

• [List elements]

Content

[Description]

Narration Notes

[Notes]

Technical Notes

• [Notes]

---

Scene 3: [Scene Name]

Duration: ~X seconds Purpose: [Purpose]

Visual Elements

• [List elements]

Content

[Description]

Narration Notes

[Notes]

Technical Notes

• [Notes]

---

[Add more scenes as needed]

---

Transitions & Flow

Scene Connections

• Scene 1 → Scene 2: [How they connect, what carries over visually]
• Scene 2 → Scene 3: [Connection]
• [Continue for all transitions]

Recurring Visual Motifs

• [Element that appears throughout, providing continuity]
• [Color or shape that reinforces key concept]

---

Color Palette

---

Mathematical Content

Equations to Render

1. [LaTeX equation 1] - used in Scene X 2. [LaTeX equation 2] - used in Scene Y 3. [Continue...]

Graphs/Plots

1. [Function 1]: domain, key features 2. [Function 2]: domain, key features

Geometric Objects

1. [Object]: properties, how it transforms 2. [Continue...]

---

Implementation Order

Suggested order for building scenes (accounting for dependencies):

1. [Scene name] - [Why first: standalone, establishes base objects] 2. [Scene name] - [Dependency notes] 3. [Scene name] - [Dependency notes] 4. [Continue...]

Shared Components

Objects or code that should be defined once and reused:

• [Component 1]: used in Scenes X, Y, Z
• [Component 2]: used in Scenes A, B

---

Open Questions / Decisions Needed

• [ ] [Question about scope, implementation, or creative direction]
• [ ] [Another decision point]

---

Reference Material

• [Link or citation to source material]
• [Inspiration videos or images]
• [Academic papers if relevant]