Markov Chains
2026-01-21
A Markov chain is fundamentally a temporal model, describing a sequence of events or states that evolve over time, where the key feature (Markov Property) is that the future depends only on the present state, not the entire past history, making it a stochastic process modeling time-dependent systems.
A Markov chain normally describes state transitions over time. Here, the chain is collapsed into space.
A finite Markov chain is evaluated once across a square field. Each tile’s state depends on the immediately preceding spatial state, not on time, according to a random but fixed transition matrix.
- The square canvas is divided into an N × N grid.
- There are K discrete states (e.g. 2–5).
- Each state corresponds to a minimal geometric primitive, like the orientation of a line or a filled / empty rectangle or a triangle orientation.
- A random K × K transition matrix defines the probability of state changes.
- The field is filled in an arbitrary but fixed scan order, here left-to-right, top-to-bottom.
- The first tile’s state is determined by the seed.
- Each subsequent tile’s state depends only on the previous tile’s state and the transition matrix.
- The image is the trace of the arbitrary scan order.
Although it computes tiles sequentially, the work is not about progression; there is no simulation of time. The scan order is merely a coordinate system, not a story. Conceptually, the image exists all at once.
Works based on Markov chains: