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Emergent Economies from Simple Agent Interactions: A Simulated Market

2025-04-02

This paper presents a simulated market economy model built from individual agent behavior. Using simple buy/sell decision rules, the model generates complex market dynamics. Each agent makes decisions based on their personal valuation of a good and their expected market price, adjusting expectations after each transaction. The simulation demonstrates convergence towards the average personal valuation, adapting to environmental changes. This offers a novel approach to dynamic economic systems in open-world RPGs, though challenges remain in addressing transaction timing and scarcity.

From Euler Angles to Quaternions: An Elegant Representation of 3D Rotations

2025-02-26

This article delves into the representation of 3D rotations. Starting with the common Euler angles, it reveals the problem of gimbal lock. It then introduces Rodrigues vectors and explains their discontinuities in representing rotations. Through analogy with lower-dimensional spaces, the article cleverly shows how to map a spherical space with antipodal point equivalence to a 4D hypersphere, ultimately introducing quaternions as a continuous and efficient representation of 3D rotations. The article also explores the application and limitations of four-axis gimbals, explaining that even adding redundant axes cannot completely avoid singularities.