About

When choices are functionally equivalent, decision paralysis sets in. This tool resolves the Buridan's Ass paradox by serving as an external entropy source. Unlike simplistic random generators, this application utilizes a Physics-Based Decay Engine coupled with Cryptographically Secure Pseudo-Random Number Generation (CSPRNG) to ensure outcomes are both mathematically fair and visually verifiable.

We employ the Web Crypto API (crypto.getRandomValues) to seed the initial angular velocity ω₀. The wheel's motion is governed by a rotational kinematic equation with a friction coefficient μ, simulating mechanical resistance. This ensures that the stopping position is non-deterministic from the user's perspective, eliminating selection bias often found in mental number picking or low-quality PRNGs.

Formulas

The core mechanic relies on integrating the angular velocity over time until kinetic energy approaches zero. The stopping condition is defined as:

t_stop = min(t) : ω(t) < ε

Where ε is a threshold close to zero (0.001 rad/s). The final angle θ determines the winning index i:

i = floor(θ mod 360360 / N)

Reference Data

Parameter	Formula / Value	Description
Angular Velocity	ω(t) = ω₀ × e^-kt	Exponential decay simulates air resistance/friction.
Sector Probability	P(x) = count(x)∑N	Probability is strictly proportional to entry frequency.
Random Seed	U ∼ [0, 2³²-1]	Derived from OS entropy pool (thermal noise/interrupts).
Sample Space	Ω = {s₁, s₂, ..., s_n}	The complete set of distinct user inputs.
Friction Coeff	μ ≈ 0.992	Calibrated for optimal suspense duration (3-6s).
Frame Rate	fps ≥ 60Hz	Managed via requestAnimationFrame.

Frequently Asked Questions

It is cryptographically random. We use the browser's `window.crypto` API, which derives entropy from hardware sources (like CPU thermal noise), making the result impossible to predict or manipulate via script logic.

Yes. The algorithm ensures uniform distribution. However, for legal audits involving significant financial value, a server-side immutable log is usually required by law. This tool runs entirely in your browser.

Yes. The probability is volume-based. If you enter "Option A" once and "Option B" nine times, "Option B" will occupy 90% of the wheel's surface area, making it 9x more likely to win.

No, the audio is reactive, not causative. The sound engine analyzes the current rotational velocity in real-time and synthesizes a "tick" sound, modulating the pitch to match the speed (Doppler effect simulation).

No. All inputs, presets, and history logs are stored locally on your device using `localStorage`. Your data never leaves your browser.

It doesn't. This is the "Wagon-wheel effect" (stroboscopic illusion). When the rotation speed matches or exceeds the screen's refresh rate (60Hz), the brain perceives the motion as reversed.