Interactive Drift Simulation
This page shows a simple 2D toy simulation of Drift Theory. Each point on the canvas is one experiential frame. The moving dot is your current state X(t). Its path is shaped by:
- Continuity: pulls the state back toward the center (plausible, smooth change).
- Emotion: bends the path toward or away from the attractor (the commitment point).
- Noise: random fluctuations, which grow with emotional intensity.
Controls
Higher emotion bends the path more strongly toward the attractor and increases volatility.
How strongly commitments (the attractor) pull your trajectory.
How much emotions amplify randomness in your path.
Smaller values ≈ finer steps; larger values ≈ faster but rougher.
Legend
- Current state X(t)
- Recent trajectory
- Attractor (commitment basin)
What This Simulation Represents
We collapse the full high-dimensional space of experience into a simple 2D toy model. The horizontal axis can be read as a coarse “physical/mundane” dimension, and the vertical axis as a coarse “relational/meaning” dimension. The attractor point represents a stable commitment (for example, staying in a relationship or honoring a promise).
Mathematically, we approximate the Drift Theory equation in discrete time:
X(t + Δt) ≈ X(t) − ∇Φ(X(t)) Δt − α · e · ∇Ψ(X(t); C) Δt + √(2 D (1 + κ e)) · ξ,
where:
- Φ is a continuity potential pulling X(t) toward the center.
- Ψ is an attractor potential pulling X(t) toward the commitment point C.
- e is the emotion slider, α and κ are the other sliders.
- ξ is a random 2D “kick” drawn from a Gaussian distribution.
This is not a full empirical model, but a visual intuition for how smooth drift, emotional curvature, and attractor basins can interact to shape a life-trajectory in experience-space.