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

This canvas visualizes an Identity Vector (Blue Dot) moving through a Narrative Field. The Red Circles are Attractor States (plot points/endings). The field exerts force on the vector.
Instructions: Click anywhere on the grid to add a new Attractor State. Adjust the sliders to change the physics of the story.

Low (Pastoral) 5.0 High (Thriller)

Controls vector velocity and field turbulence.

Weak Plot 8.0 Inevitable Fate

Strength of plot points to pull the character.

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

In Narrative Geometry, a character is not static. As the Identity Vector moves through the field, the field exerts deformation forces on the vector.

This means characters must change to satisfy the geometric constraints of the plot. Use the slider below to observe how high-intensity fields warp an identity from its initial state ($t_0$) to a resolved state ($t_n$).

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

Narrative Diffusion & Refinement

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

Equation 2.1: Field Potential
V(x) = - Σ ( G_i / |x - A_i|^λ )
Where A_i are Attractor States and λ is the Intensity Scalar controlling the steepness of the potential well.
Figure 3: Inverse relationship between Narrative Entropy and Structural Coherence over time.

Applications

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

🤖

AI Storytelling Engines

Using the Story Tensor to ensure generative text models (LLMs) adhere to long-term plot consistency rather than just statistical token prediction.

🎭

Dynamic NPCs

Video game characters with "Identity Vectors" that naturally evolve based on player interactions and field conditions, creating emergent character arcs.

📊

Reputation Modeling

Mapping brand or personal reputation as a vector in a public "narrative field," predicting how specific events (attractors) will shift public perception.