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Official Documentation & System Reference

Ulamora Studio Documentation

Everything you need to construct, simulate, inspect, and export interactive scientific pipelines in AI, Quantum Computing, Linear Algebra, and Dynamical Physics.

01. Architecture 02. AI Nodes 03. Quantum Nodes 04. Math Nodes 05. Physics Nodes 06. .ulamora Format 07. Shortcuts
// 01 System Architecture

Pure-Client DAG Execution Engine

DAG

Directed Acyclic Graph

Pipelines are scheduled using Kahn's topological sort algorithm, ensuring zero cyclic deadlocks and strictly deterministic execution order across all computational units.

SIMD

Zero-Backend Compute

All numerical simulations (SVD, 2D FFT, Quantum statevectors, Runge-Kutta & Symplectic Euler solvers) execute 100% locally inside the browser. No data ever leaves your computer.

1:1

Cross-Runtime Parity

Every pipeline can be exported to clean, dependency-free Python NumPy code or modern ECMAScript. Verified numerical parity between browser runtime and terminal execution.

// 02 AI & Transformer Architecture

AI & Neural Nodes

Text Prompt / Corpus ai_prompt

Source text corpus input node for language models and tokenizers.

Inputs: None (Source Generator)
Outputs: text (string)
Parameters: text (Default: 'Quantum attention computes deep spacetime vectors')
Subword Tokenizer ai_tokenizer

Performs deterministic subword tokenization with reproducible hash vocabulary encoding.

Inputs: text (string)
Outputs: tokens (token ID array)
Vocab Size: 10,000 subwords
Token Embedding Matrix ai_embedding

Maps discrete token IDs into dense continuous semantic vector embeddings.

Inputs: tokens (array)
Outputs: matrix ($N \times d_{\text{model}}$ tensor)
Parameters: dim (e.g. 8, 16, 32, 64)
Linear Projection ($W_q, W_k, W_v$) ai_linear_proj

Projects embedding vectors into dedicated Query, Key, or Value subspace representations.

Formula: $Q = X W_q,\; K = X W_k,\; V = X W_v$
Inputs: matrix ($N \times d$)
Outputs: proj ($N \times d_{\text{proj}}$)
Parameters: projType ('Q', 'K', 'V')
Scaled Dot-Product Self-Attention ai_attention

Computes query-key compatibility scores, softmax normalization, and contextual value aggregation.

$$\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{Q K^T}{\sqrt{d_k}} + M\right) V$$
Inputs: q, k, v ($N \times d$)
Outputs: weights ($N \times N$ attention matrix), context ($N \times d$ context matrix)
Parameters: causalMask (true/false)
// 03 Quantum Mechanics & Circuits

Quantum Computing Nodes

Quantum Register quantum_circuit

Initializes an $n$-qubit register in the canonical ground state $|0\rangle^{\otimes n}$ with statevector length $2^n$.

Outputs: circuit (QuantumCircuit state)
Parameters: qubits (1 to 6 qubits)
Hadamard Gate (H) quantum_hadamard

Creates an equal superposition between computational basis states $|0\rangle$ and $|1\rangle$.

Gate Matrix: $H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$
Inputs: circuit
Outputs: circuit
Parameters: targetQubit (0-indexed)
Controlled-NOT (CNOT / CX) quantum_cnot

Entangles two qubits by flipping the target qubit conditioned on the control qubit state.

Action: $|c, t\rangle \mapsto |c, c \oplus t\rangle$
Parameters: controlQubit, targetQubit
Measurement & State Profile quantum_measurement

Extracts Born rule measurement probability distribution $P(x) = |\langle x | \psi \rangle|^2$ and reduced density states.

Outputs: probabilities ($2^n$ array), statevector
// 04 Linear Algebra & Matrix Calculus

Math & Linear Algebra Nodes

Matrix Input (Tensor Generator) math_matrix

Produces 2D continuous matrix tensors via deterministic random seeds, identity, or custom shapes.

Outputs: matrix ($M \times N$)
Parameters: rows, cols, fillType ('random', 'zeros', 'identity')
Matrix Multiplication (MatMul) math_matmul

High-performance row-major linear algebra matrix product $C = A \cdot B$.

Formula: $C_{ij} = \sum_{k=1}^K A_{ik} B_{kj}$
Inputs: a ($M \times K$), b ($K \times N$)
Outputs: c ($M \times N$)
Singular Value Decomposition (SVD) math_svd

Decomposes matrix $A$ into unitary matrices $U, V^T$ and diagonal singular values $\Sigma$ for spectral analysis and low-rank compression.

$$A = U \Sigma V^T = \sum_{i=1}^r \sigma_i u_i v_i^T$$
Inputs: matrix ($M \times N$)
Outputs: u ($M \times K$), s ($K$ singular values), vt ($K \times N$)
WebGPU Hardware MatMul gpu_matmul

Hardware-accelerated matrix multiplication running on native WebGPU WGSL compute shader with seamless client-side CPU SIMD fallback.

$$C = \alpha (A \times B), \quad C_{ij} = \sum_{k=1}^K A_{ik} B_{kj}$$
Inputs: a ($M \times K$), b ($K \times N$)
Outputs: result ($M \times N$), telemetry (GFLOP/s, Latency)
// 05 Physics & Numerical Integrators

Dynamical Systems & Physics Nodes

3-Body Gravitational Dynamics physics_nbody

Simulates chaotic gravitational motion using a energy-conserving Symplectic Euler (Semi-Implicit Euler) numerical integrator.

Integrator: $v_{t+\Delta t} = v_t + a(x_t)\Delta t,\; x_{t+\Delta t} = x_t + v_{t+\Delta t}\Delta t$
Outputs: bodies (array of orbital bodies, KE, and positions)
Parameters: preset ('figure8', 'lagrange', 'sun_earth_moon', 'pythagorean')
2D Wave PDE Mesh Solver physics_wave_2d

Finite-difference time-domain (FDTD) discrete solver for the acoustic/membrane wave PDE.

Equation: $\frac{\partial^2 u}{\partial t^2} = c^2 \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right) - \gamma \frac{\partial u}{\partial t}$
Outputs: wave ($48 \times 48$ amplitude surface)
2D Fast Fourier Transform (FFT) math_fft_2d

Transforms 2D spatial grid signals into frequency-domain k-space magnitude spectra.

Formula: $X_{u,v} = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} x(x,y) e^{-j 2\pi (\frac{ux}{M} + \frac{vy}{N})}$
Inputs: wave ($M \times N$)
Outputs: magnitude ($M \times N$)
Lorenz Strange Attractor (Chaos) physics_lorenz

Continuous chaotic convection ODE system solved with 4th-order Runge-Kutta (RK4).

ODEs: $\dot{x} = \sigma(y - x),\; \dot{y} = x(\rho - z) - y,\; \dot{z} = xy - \beta z$
Outputs: trajectory ($T \times 3$ orbital coordinates)
Molecular Dynamics (Lennard-Jones) physics_molecular_dynamics

Simulates N-particle thermodynamic ensembles using truncated Lennard-Jones (12-6) potential, periodic boundary conditions (PBC), and symplectic Velocity-Verlet integration.

$$V(r) = 4\epsilon \left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6\right], \quad \mathbf{r}(t+\Delta t) = \mathbf{r} + \mathbf{v}\Delta t + \frac{1}{2}\mathbf{a}\Delta t^2$$
Outputs: particles (atoms list), thermo ($T, P, KE, PE, E_{tot}$), positions
Parameters: numParticles, boxSize, temperature, thermostat
Reaction-Diffusion (Turing PDE) physics_reaction_diffusion

Solves Alan Turing's nonlinear coupled Gray-Scott reaction-diffusion biophysical PDE on a discrete 2D Laplacian grid with WebGPU acceleration.

$$\frac{\partial u}{\partial t} = D_u \nabla^2 u - uv^2 + F(1-u), \quad \frac{\partial v}{\partial t} = D_v \nabla^2 v + uv^2 - (F+k)v$$
Outputs: grid_u, grid_v ($N \times N$ morphogens), entropy
Parameters: regime ('mitosis', 'coral', 'solitons', 'waves', 'stripes')
// 06 File Format Specification

The .ulamora Pipeline Format

Ulamora pipelines are stored as lightweight, human-readable JSON files using the standardized .ulamora file extension (or standard .json). Files contain complete node topologies, coordinates, custom parameters, and camera viewports. 

{
  "format": "ulamora",
  "version": "1.0.0",
  "generator": "Ulamora Studio (ulamora.com)",
  "name": "Transformer Self-Attention Pipeline",
  "timestamp": 1727450000000,
  "view": {
    "panX": 30,
    "panY": 70,
    "zoom": 0.82
  },
  "nodes": [
    {
      "id": "node_prompt",
      "type": "ai_prompt",
      "title": "Text Prompt / Corpus",
      "category": "ai",
      "x": 60,
      "y": 180,
      "params": {
        "text": "Quantum attention computes deep spacetime vectors"
      }
    }
  ],
  "connections": [
    {
      "fromNode": "node_prompt",
      "fromPort": "text",
      "toNode": "node_tokenizer",
      "toPort": "text"
    }
  ]
}
// 07 Productivity & Gestures

Keyboard Shortcuts & Canvas Navigation

Action Shortcut (macOS) Shortcut (Windows / Linux)
Run Pipeline ⌘ + Enter Ctrl + Enter
Browse Templates ⌥ + T Alt + T
Save Project ⌘ + S Ctrl + S
Open Project ⌘ + O Ctrl + O
Toggle Node Library ⌥ + L Alt + L
Toggle Inspector ⌥ + I Alt + I
Search Nodes / /
Toggle Console ~ ~

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