QUANTUM LAB | High-Performance Scientific, Cryptographic & Algorithmic Workbench

Arbitrary-Precision Number Theory Engine

Execute Miller-Rabin primality verifications, Pollard's rho integer factorization, greatest common divisor via Euclidean algorithm, and modular exponentiation.

Number Parameters

Number A (Target for Primality & Factorization)

Number B (Exponent or Second Operand)

Modulus M (For a^b mod m)

Number Theoretical Properties

Primality Status (Miller-Rabin) PROBABLE PRIME

Prime Factorization 982451653

Greatest Common Divisor GCD(A, B) 1

Least Common Multiple LCM(A, B) 64386923081661

Modular Power (A^B mod M) 348625907

Euler's Totient φ(A) 982451652

High-Performance Linear Algebra & Matrix Decomposition

Gaussian elimination with partial pivoting, LU decomposition, matrix inversion, trace, rank, and dominant eigenvalue approximation via power iteration.

Matrix A Grid

Dimension:

Matrix Invariants & Spectral Properties

Determinant det(A) 105.000000

Trace tr(A) 15.0000

Matrix Rank 3

Dominant Eigenvalue λ 7.245892

Normalized Eigenvector v [0.4521, 0.3812, 0.8066]

Inverse Matrix A⁻¹

--

LU Factorization (L / U)

L Factor

U Factor

Numerical Calculus & Runge-Kutta 4th Order ODE Solver

Composite Simpson quadrature numerical integration, central difference differentiation, Newton-Raphson root discovery, and RK4 initial value problem solver.

Function Calculus & Root Finding

Mathematical Expression f(x)

Integration Start a

Integration End b

Evaluation Point x

Definite Integral ∫ f(x) dx 1.87241804

First Derivative f'(x) -0.08544917

Second Derivative f''(x) -0.84594680

Newton Root Discovery 3.14159265

RK4 ODE Trajectory Plotter: dy/dx = f(x, y)

Differential Equation dy/dx

x0

y0

xEnd

Step h

Ready to solve

Cooley-Tukey Radix-2 Fast Fourier Transform (FFT)

Discrete Fourier spectral decomposition with Hann/Hamming windowing functions, real-time waveform generation and frequency bin power analysis.

Signal Configuration

Fundamental Frequency f1 (Hz)

Harmonic Frequency f2 (Hz)

Amplitude A1

Amplitude A2

Window Function

Peak Dominant Frequency 35.0 Hz

Nyquist Sampling Metrics 1.00 Hz/bin (Nyquist: 512 Hz)

Time Domain Waveform [x(t)]

Frequency Domain Magnitude Spectrum [|X(f)|]

Combinatorics, Stirling Numbers & Integer Partitions

High-precision evaluation of Bell numbers, Stirling partition numbers of the second kind, subfactorials (derangements), binomial coefficients and Euler partitions.

Parameters (n, k)

Set Cardinality n

Subset Partition Size k

Exact Combinatorial Values

Factorial n! 479001600

Permutations P(n, k) 95040

Binomial Coefficient C(n, k) 792

Derangements !n 176214841

Stirling 2nd Kind S(n, k) 1379400

Bell Number B(n) 4213597

Integer Partitions p(n) 77

Cryptographic Hash Functions & Message Authentication

Pure JavaScript implementation of SHA-256 (FIPS 180-4), MD5 (RFC 1321), CRC-32 (IEEE 802.3), and Hash-based Message Authentication Codes (HMAC).

Cryptographic Input Stream

Message Payload

HMAC Secret Key

SHA-256 Digest (256-bit FIPS 180-4) --

HMAC-SHA256 Authentication Code --

MD5 Digest (128-bit RFC 1321) --

CRC-32 Checksum (IEEE 802.3) --

Symmetric Cipher Internal State & Round Transformations

Interactive visualization of AES-128 round transformations (SubBytes S-Box, ShiftRows, MixColumns Galois Field arithmetic) and ChaCha20 quarter-rounds.

AES-128 4x4 State Matrix [Bytes]

ChaCha20 Quarter-Round Simulation

Executes the ARX (Add-Rotate-Xor) primitive on 32-bit registers (a, b, c, d).

Click Run to evaluate ChaCha20 state

AVL Self-Balancing Trees & Dijkstra Shortest Path

Interactive AVL binary search tree visualizer with automatic tree rotations, and weighted graph pathfinder using Dijkstra's greedy algorithm.

AVL Self-Balancing Tree View

In-Order Sort: --

Weighted Graph & Dijkstra Pathfinder

→

Shortest Route: A -> B -> D -> F

Cost: 15

Binary Hex Dumper & JWT Authentication Inspector

Hexadecimal memory dump with ASCII sidecar, JSON Web Token (JWT) payload decoder, and multi-format binary/base64/URL converters.

Hexadecimal Memory Stream Viewer

Input Plaintext Stream

JWT Token Payload Unpacker

JSON Web Token

Header

--

Payload

--

Signature: --

Multi-Format Encoding Transformer

Input String

Base64 Encoded

URL Percent Encoded

Binary Bitstream (8-bit)

Hexadecimal Bytes

Modular Polyphonic Synthesizer & Web Audio DSP

Real-time Web Audio API sound synthesis with polyphonic oscillators, ADSR envelopes, resonant biquad filtering, feedback delay, and audio analyzers.

Synthesizer Keyboard (C4 - E5)

Waveform

Filter Cutoff: 1800 Hz

Filter Resonance Q: 4

Attack: 0.05s

Release: 0.3s

Master Volume: 0.4

Real-Time Oscilloscope Waveform

Fast Fourier Spectrum Bars

N-Body Gravitational Orbital Simulator

Deterministic Newtonian gravity solver with Velocity Verlet integration. Drag on canvas to deploy satellites with initial velocity vectors.

2D Optical Bench Raytracer & Chromatic Dispersion

Simulation of Snell's Law of refraction (n1 sin θ1 = n2 sin θ2), chromatic dispersion across triangular glass prisms, and planar mirror reflection.

Laser Emitter Controls

Laser Beam Angle (Radians)

Emitter Vertical Position Y

Refractive Dispersion Indices

Red (680nm): n = 1.51
Green (530nm): n = 1.52
Blue (440nm): n = 1.53

Conway's Game of Life Cellular Automata

Toroidal 2D grid cellular automaton evaluating neighbor survival and birth rules with Gosper Glider Gun and oscillator presets.

Kinetic Gas Theory & Maxwell-Boltzmann Distribution

2D hard-sphere molecular particle collision dynamics demonstrating elastic conservation of momentum and emergent thermal pressure.

Thermodynamic Metrics

Heat / Kinetic Velocity Scaling

Temperature T 300.0 K

Wall Pressure P 42.50 kPa

Speed Distribution Histogram

RLC Series AC Impedance & Resonance Solver

Complex impedance calculation Z = R + j(XL - XC), resonance frequency, circuit Q-factor, bandwidth, and reactive/apparent power.

Circuit Components

Resistance R (Ω)

Inductance L (mH)

Capacitance C (μF)

AC Frequency f (Hz)

AC Source RMS Voltage (V)

Impedance & AC Electrical State

Total Impedance |Z| 102.32 Ω (Phase: 12.4°)

Resonance Frequency f0 876.54 Hz

Inductive Reactance XL 94.25 Ω

Capacitive Reactance XC 72.34 Ω

Circuit Q-Factor 0.826

RMS Current I 117.28 mA

Active & Apparent Power 1.375 W (S: 1.407 VA)

NE555 Timer & Operational Amplifier Engineering

Calculate astable 555 oscillation frequency, duty cycles, high/low state timing, inverting and non-inverting operational amplifier gains.

NE555 Astable Multivibrator

R1 (kΩ)

R2 (kΩ)

C (μF)

Oscillation Frequency 138.46 Hz

Duty Cycle 54.8 %

High Time tH 3.950 ms

Low Time tL 3.257 ms

Operational Amplifier Circuit

Configuration

Rf (kΩ)

Rin / R1 (kΩ)

Vin (V)

Closed-Loop Voltage Gain Av -10.00x

Output Voltage Vout -5.000 V

Digital Logic Gates & Binary Full Adder

Interactive logic gates with clickable binary pins and full adder truth table computation.

Configurable Logic Gate

Input Pin A: 0 Input Pin B: 1

Output: 0

Click on pins 0/1 to toggle logic level.

1-bit Binary Full Adder Circuit

A: 1 B: 1 Cin: 0

FULL ADDER

Sum: 0 Cout: 1

Evaluates: Sum = A ⊕ B ⊕ Cin; Cout = (A · B) + (Cin · (A ⊕ B)).

Black-Scholes-Merton European Options & Greeks

Analytical European call and put option valuation, first- and second-order Greeks (Delta, Gamma, Vega, Theta), and expiration payoff diagram.

Option Pricing Parameters

Underlying Asset Price S ($)

Strike Price K ($)

Time to Maturity T (Years)

Risk-Free Rate r (%)

Implied Volatility σ (%)

Option Theoretical Prices & Risk Greeks

Call Option Price $10.42

Put Option Price $3.21

Call Delta Δ 0.6842

Put Delta Δ -0.3158

Gamma Γ 0.0215

Vega ν (per 1%) 0.2451

Theta Θ (daily) -0.0248

Expiration Payoff & P&L Profile

Monte Carlo Portfolio Risk & Value at Risk (VaR)

Stochastic Geometric Brownian Motion simulation modeling price trajectories, Value at Risk (95% / 99%) and Conditional Expected Shortfall (CVaR).

GBM Stochastic Model Inputs

Initial Portfolio Value S0 ($)

Annual Expected Return μ (%)

Annual Asset Volatility σ (%)

Simulation Horizon (Trading Days)

95% Value at Risk (VaR) $11,450.00

99% Value at Risk (VaR) $18,220.00

95% CVaR (Expected Loss) $14,890.00

Expected Portfolio Mean $102,400.00

Monte Carlo Simulated Asset Trajectories

Fixed-Rate Loan Amortization Schedule

Actuarial debt service amortization schedule breakdown between principal reduction, interest cost, and remaining unpaid balance.

Loan Specification

Principal Amount ($)

Annual Interest Rate (%)

Loan Term (Years)

Monthly Payment (P&I) $2,270.21

Cumulative Interest Paid $467,275.60

Total Cost of Debt $817,275.60

Amortization Table (First 24 Months)

Month	Payment	Principal	Interest	Balance

IPv4 CIDR Subnet Calculator & Bitmask Visualizer

Binary octet bitmask decomposition, netmask, wildcard mask, broadcast address, and assignable host address range analysis.

CIDR Address Definition

IP Address / CIDR Prefix

Binary Bitmask Stream (Network vs Host Bits)

Network Address 192.168.10.0

Subnet Mask 255.255.255.192

Wildcard Mask 0.0.0.63

Broadcast Address 192.168.10.63

Usable Host Range 192.168.10.1 - 192.168.10.62

Usable Hosts Count 62

Color Spaces Converter & WCAG 2.1 Accessibility Auditor

Bi-directional conversions between HEX, RGB, HSL, CMYK color spaces and relative luminance contrast calculations.

Color Input

Hexadecimal Code

#00D2FF

Color Coordinate Transformations

RGB Tuple rgb(0, 210, 255)

HSL Cylindrical hsl(191°, 100%, 50%)

CMYK Subtractive cmyk(100%, 18%, 0%, 0%)

WCAG 2.1 Contrast Ratio Audit

Contrast on Pure White (#FFFFFF) 1.75:1 (Fail)

Contrast on Terminal Dark (#0A0E17) 12.05:1 (AA Pass)

JSON Validator, SQL Beautifier & Cron Humanizer

Format structured JSON payloads, indent SQL relational queries, and decode standard 5-part UNIX cron expressions.

JSON Validator & Beautifier

SQL Query Beautifier

UNIX Cron Expression Humanizer

Cron Expression (min hour day month weekday)

Interpreted Schedule --