Plotting parametric curves.

A vertical vector of decimal numbers representing an embedding. Displays values with color coding based on magnitude.

A reusable spring-mass system component with physics simulation. This is a great example of 3b1b's approach: create a self-contained VGr

Animation that leaves a trail of fading dots at specified positions.

A matrix of decimal numbers with color-coded entries. Used to represent weight matrices in neural networks.

Attention pattern grid.

A grid showing attention pattern with dots.

Animation showing context flow from source words to target word. Creates arcing lines that flash from sources to target.

A column vector (embedding) with color-coded entries.

A column vector displaying numeric values.

Animation that randomizes a ValueTracker's value at a given frequency.

A simple 3D-style embedding column.

Tracks the state of the block collision process.

Tracks the state of the block collision process.

A visual effect that makes multiple pieces appear to be in superposition. The pieces jitter/oscillate around their center positions with a g

Animation that leaves a trail of fading dots at specified positions.

A matrix displaying weight values with color coding.

Animation showing context flowing between tokens.

A simple neural network visualization with layers and connections.

A column vector (embedding) with color-coded entries.

Animation that randomizes a ValueTracker's value at a given frequency.

A simple numeric embedding visualization.

A simplified numeric embedding visualization.

Tracks the state of the block collision process as a 4d vector [ x1 * sqrt(m1), x2 * sqrt(m2), v1 * sqrt(m1),

Tracks the state of the block collision process.

A matrix with color-coded entries based on value.

A matrix with color-coded entries based on value.

Template for aligned equations.

Shows probability distribution bars animating as context changes. Demonstrates how the distribution shifts based on input.

Animating a function parameter change.

Surface that changes over time.

Demonstrates combining multiple animations.

Template showing various animation types.

Basic visualization of definite integral as area under curve. Shows smooth accumulation of area from left to right.

Visualizing area under a curve (integration).

Arrow that always points from one object to another.

3D version of attention arcs with camera movement.

Demonstrates attention mechanism through animated arcs connecting positions. This visualization shows how each position attends to other pos

Shows how attention scores form a matrix pattern.

Visual representation of attention weights between tokens. Shows which tokens attend to which with varying line widths.

Demonstrates how attention allows words to influence each other. Shows adjectives modifying nouns through attention connections.

Shows how text flows through a transformer-like machine, demonstrating the autoregressive generation process.

Show that unit integrals equal the average value over that interval. Helps build intuition for the Laplace transform.

Basic 3D scene with shapes.

Basic axes setup and labeling.

A basic scene template showing common patterns. Modify this template for your needs: - Add your mobjects in construct() - Create ani

Simple updater that makes an object follow another.

Simplified beam splitter demonstration.

Shows bit strings with ket notation.

Visualize a quantum state as a vector on the Bloch sphere.

Mass ratio 10000:1 gives 314 collisions

Mass ratio 1000000:1 gives 3141 collisions

A simplified block collision demonstration. Shows two blocks colliding elastically.

3D visualization of colliding blocks with floor and wall.

Explains the Born rule for quantum measurement.

Uses braces to annotate and explain equation parts. Another signature 3b1b technique.

Template combining equations with visual elements.

Demonstrating 3D camera controls.

Shows how the change of basis matrix S transforms coordinates between standard basis and eigenbasis.

Shows the geometric puzzle: counting lines bouncing between a circle and a line. This is the geometric interpretation of the collision counti

Circle that grows/shrinks with a ValueTracker.

Shows the classic neural network diagram with connected nodes. Inputs feed into hidden layer neurons which connect to outputs. Demonstra

Shows block collisions with a phase space diagram. The state point traces a path on a circle as collisions occur.

Demonstrates color-coding for syntax highlighting in equations.

Shows variable substitution with color tracking. Makes complex substitutions easy to follow.

Demonstrates color manipulation and gradients.

Template for color-coded mathematical expressions.

Visualize e^{(a+bi)t} as a spiral in the complex plane. Shows how real part controls growth/decay, imaginary controls rotation.

Shows e^((a+bi)t) = e^(at) * e^(bit) as an exponential spiral. When a < 0, we get a decaying spiral (damped oscillation).

Template for complex number visualization.

A cone that unfolds into a flat sector. Demonstrates surface transformation.

Advanced coordinate labeling techniques.

Shows how e^(it) + e^(-it) = 2cos(t). Two counter-rotating vectors that sum to give real cosine.

Shows cross-attention between two languages.

Demonstrates projecting a 3D cube along its main diagonal [1,1,1]. Shows: 1. Building the cube from vertices 2. Showing coordinates

Interactive visualization of damped spring solutions on the s-plane. The characteristic equation ms^2 + μs + k = 0 has roots that: - Sta

Shows the chain rule for derivatives.

Shows the key insight: diagonal matrices are easy to raise to powers. This makes computing A^n efficient when A is diagonalizable.

Simplified diffraction grating visualization showing multiple slits.

Shows dot product calculation between two vectors in 2D. The result updates dynamically as vectors are rotated.

Visualizes the double-slit experiment with wave interference. Shows plane wave hitting two slits and producing interference.

Shows state vector evolving and probabilities updating in real-time.

Displays the fundamental eigenvalue/eigenvector equations with proper color coding to highlight mathematical relationships.

Shows the vector field for a linear ODE system dx/dt = Ax. The eigenvectors are the special directions where trajectories move straight o

Shows a matrix transformation in two perspectives: 1. Standard basis (i-hat, j-hat) - complex shearing transformation 2. Eigenbasis - sim

Shows that eigenvectors only get scaled by their eigenvalue. Multiple vectors are shown - eigenvectors stay on their line, other vectors

Visualization of elastic collision with velocity vectors. Shows conservation of kinetic energy and momentum.

Electric field from two point charges (dipole).

Shows multiple embeddings arranged as an array/matrix.

Visualizes the embedding matrix concept: - Words as columns - Each column is a word's vector representation

Shows step-by-step equation derivation with highlighting.

The famous e^(i*pi) = -1 visualization. Shows how rotating by pi radians lands at -1.

Visual demonstration of the exponential function's defining property. Key techniques: - get_v_line_to_graph for vertical lines - get

Show family of exponentials e^{st} for different values of s. When s > 0: growth, s < 0: decay, s = 0: constant.

Visualize the integral of e^(-x) from 0 to infinity. Shows that the total area is exactly 1.

Shows how a threshold on the dot product creates a decision boundary. Positive side = "Yes", Negative side = "No". Demonstrates: Regions

Derives the closed-form Fibonacci formula using eigenvalues. F_n = (phi^n - psi^n) / sqrt(5)