3Blue1Brown Style Mathematical Animations
Use this skill when creating mathematical animations, visualizations, or educational videos about math, algorithms, or deep learning.
Core Philosophy
"The goal is not to animate math, but to build understanding."
- Intuition Before Formalism — Build visual understanding before showing formulas
- Why Before What — Motivate concepts before defining them
- Concrete Before Abstract — Start with specific examples, then generalize
- Show, Don't Tell — Let the visual do the explaining
When to Use
- Creating mathematical animations with Manim
- Explaining algorithms visually
- Building deep learning visualizations
- Producing educational video content
AI-Guided Planning (REQUIRED)
Before starting any video, follow this workflow:
Step 1: Draft Plan Internally
When user requests an animation:
- Understand the topic
- Draft content structure
- Identify visual elements needed
Step 2: Ask User Preferences
Use AskUserQuestion tool to gather preferences:
questions = [
{
"question": "Do you want narration audio in this video?",
"header": "Audio",
"options": [
{"label": "With Audio (Recommended)", "description": "TTS narration synced to animation"},
{"label": "Without Audio", "description": "Animation only, add your own audio later"}
],
"multiSelect": False
},
{
"question": "How long should the video be?",
"header": "Duration",
"options": [
{"label": "Short (30-60s)", "description": "Quick concept overview"},
{"label": "Medium (1-2 min)", "description": "Standard explanation"},
{"label": "Long (3+ min)", "description": "Deep dive with examples"},
{"label": "Auto (Recommended)", "description": "Let content determine length"}
],
"multiSelect": False
}
]
Step 3: Present Plan for Approval
Show the content plan before coding:
📋 Animation Plan: [Topic]
1. Hook: [Opening question]
2. Setup: [Context]
3. Core: [Main explanation]
4. Example: [Demonstration]
5. Takeaway: [Conclusion]
Settings: Audio=Yes, Duration=Auto (~70s)
Shall I proceed?
Step 4: Execute Based on Choices
| Choice | Workflow |
|---|
| With Audio | Script → TTS → Measure Duration → Code Animation → Render → Combine |
| Without Audio | Estimate Timing → Code Animation → Render |
Key Principles
Duration is NOT Fixed
# ❌ WRONG: Force fixed duration
duration = 60 # arbitrary
# ✅ RIGHT: Content determines duration
script = write_explanation(topic)
duration = measure(script) # natural length
Always Ask, Never Assume
- Audio preference
- Duration preference
- Detail level (if relevant)
Rules Index
Highest Priority: Quality & Planning
| Rule | Description |
|---|
rules/visual-quality.md | CRITICAL - No overlaps, readable text, clear hierarchy |
rules/pre-production.md | AI-guided planning with user interaction |
rules/layout-spacing.md | Screen zones, spacing, margins |
High Priority: Pedagogy & Content
| Rule | Description |
|---|
rules/pedagogy.md | Teaching philosophy and explanation structures |
rules/mathematical-rigor.md | Ensuring mathematical correctness |
rules/narrative-flow.md | Smooth transitions and completeness |
rules/audio-sync.md | Synchronizing narration with visuals |
Visual Design
| Rule | Description |
|---|
rules/color-scheme.md | 3b1b color palette and semantic meaning |
rules/scene-basics.md | Animation timing and sequencing |
rules/camera-work.md | Focus, zoom, and visual hierarchy |
Domain: Linear Algebra
| Rule | Description |
|---|
rules/linear-transformations.md | Geometric interpretation of transforms |
rules/matrix-operations.md | Matrix multiplication visualization |
rules/eigenvalues.md | Eigenvector and eigenvalue intuition |
rules/vector-space.md | Vector operations and spaces |
Domain: Statistics & Probability
| Rule | Description |
|---|
rules/distributions.md | PDF/CDF visualization |
rules/bayes-theorem.md | Bayesian reasoning |
rules/sampling.md | Monte Carlo methods |
Domain: Deep Learning
| Rule | Description |
|---|
rules/neuron.md | Single neuron visualization |
rules/layer.md | Layer representations |
rules/network-architecture.md | Full network diagrams |
rules/forward-pass.md | Data flow visualization |
rules/gradient-flow.md | Backpropagation visualization |
rules/attention.md | Attention mechanism |
rules/transformer-block.md | Transformer architecture |
Domain: CNN
| Rule | Description |
|---|
rules/convolution.md | Convolution operation |
rules/feature-maps.md | Feature map visualization |
rules/pooling.md | Pooling operations |
Technical
| Rule | Description |
|---|
rules/manim-setup.md | Installation and configuration |
rules/narration.md | TTS integration and script writing |
Example Interaction
User: "quick sort 애니메이션 만들어줘"
AI: [Internal: Draft plan for QuickSort]
AI: [AskUserQuestion]
"I'll create a QuickSort animation. Quick questions:
1. Audio: With narration / Without
2. Duration: Short / Medium / Auto"
User: "audio 있고, auto로"
AI: "Here's my plan:
📋 QuickSort Animation
1. Hook: How do we sort efficiently?
2. Setup: Unsorted array
3. Core: Pivot selection, partitioning
4. Example: Sort [8,3,7,1,5,2]
5. Takeaway: O(n log n) average
Duration: ~90s (based on narration)
Proceed?"
User: "네"
AI: [Executes workflow]
→ Generates TTS
→ Measures timing
→ Creates animation
→ Renders & combines
→ Shows result
Quick Start Code
from manim import *
class ExplanationScene(Scene):
def construct(self):
self.camera.background_color = "#1c1c1c"
# Sync to audio timing (if audio enabled)
# TIMING = {...} # from TTS generation
# 1. Hook: Pose the question
# 2. Intuition: Build visual understanding
# 3. Formalize: Show the math
# 4. Verify: Demonstrate with example
