Narrative Geometry

A computational field theory defining narratives as causal fields and identities as vectors. By mapping story structures to geometric attractors, we can model character arcs as physical trajectories through a "Story Tensor."

Field Theory
Stories are environments, not just sequences. They exert "force" on characters.
Identity Vectors
Characters are mathematical vectors that mutate when passing through narrative fields.
Computational AI
A framework for generative agents that behave with geometric consistency.

1. Formal Definitions

Before simulating the field, we must define the axioms of Narrative Geometry. In this framework, literary concepts are translated into physics-based counterparts. Click the cards below to explore the core components.

T

Story Tensor

The matrix containing all possible states, transitions, and rules of the narrative universe.

F

Narrative Field

The local manifestation of the tensor. It exerts "narrative gravity" pulling agents toward attractors.

V

Identity Vector

The agent. A multi-dimensional vector representing traits, memories, and current state.

λ

Intensity Scalar

A modulation value determining the "heat" or pressure of the field. High λ forces rapid mutation.

Select a concept above...

Interactive explanations will appear here.

Interactive Lab

Narrative Field Simulator

Visualize an Identity Vector (Blue Dot) moving through a Narrative Field. Red Circles are Attractor States (plot points).
Instructions: Click grid to add Attractors. Use sliders to change physics.

Low (Pastoral) 5.0 High (Thriller)
Weak Plot 8.0 Inevitable Fate
Fluid (Dream) 0.3 Rigid (Hard Sci-Fi)
Vector Position: 0, 0
Velocity: 0
Distance to Goal: N/A
Click to add Attractor

Identity Mutation

Select an Archetype to load predefined vector states. Drag the slider to observe how the narrative field warps the identity from $t_0$ (Start) to $t_n$ (Resolution).

Inciting Incident ($t_0$) Climax Resolution ($t_n$)
Current State
Initial Baseline

Narrative Diffusion

Just as diffusion models denoise an image, narrative fields "denoise" a plot. At the start, probability space is vast (high entropy). Attractors collapse possibilities into a coherent path.

Equation 2.1: Field Potential
V(x) = - Σ ( G_i / |x - A_i|^λ )
Where A_i are Attractors and λ is Intensity.
Figure 3: Inverse relationship between Narrative Entropy and Structural Coherence.

Applications

Narrative Geometry provides a rigorous mathematical foundation for next-generation AI systems.

🤖

AI Storytelling

Ensuring generative text models (LLMs) adhere to long-term plot consistency via geometric constraints.

🎭

Dynamic NPCs

Video game characters with "Identity Vectors" that evolve based on player interactions.

📊

Reputation Models

Mapping reputation as a vector in a public "narrative field," predicting perception shifts.