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Related Experiment Video

Updated: Jun 25, 2026

3D Modeling of Dendritic Spines with Synaptic Plasticity

3D Modeling of Dendritic Spines with Synaptic Plasticity

Published on: May 18, 2020

A stochastic adding machine and complex dynamics.

Peter R Killeen¹, Thomas J Taylor

¹Department of Psychology, Arizona State University, Tempe, AZ 85287, USA.

|March 7, 2009

Summary

This summary is machine-generated.

This study explores a Markov chain modeling a binary adding machine with potential failures. Its transition operators exhibit self-similarity, with spectra related to complex Julia sets.

Related Experiment Videos

Last Updated: Jun 25, 2026

3D Modeling of Dendritic Spines with Synaptic Plasticity

3D Modeling of Dendritic Spines with Synaptic Plasticity

Published on: May 18, 2020

Area of Science:

Stochastic processes
Dynamical systems
Number theory

Background:

Markov chains are fundamental in modeling systems with probabilistic transitions.
Binary adding machines are computational devices with specific operational rules.
Understanding failure probabilities is crucial for reliable system modeling.

Purpose of the Study:

To analyze the properties of a Markov chain modeling a binary adding machine with failure.
To investigate the structure of related quotient Markov chains and extensions to 2-adic integers.
To characterize the spectral properties of the transition operators.

Main Methods:

Definition and analysis of a Markov chain on natural numbers.
Construction of quotient Markov chains.
Extension of the chain to 2-adic integers.
Investigation of the self-similar structure of transition operators.

Main Results:

The Markov chain exhibits a non-zero probability of failure during register increments.
A family of natural quotient Markov chains is identified.
The chain extends to the 2-adic integers.
The transition operators possess self-similar structures.
The spectra are identified as Julia sets or filled Julia sets of quadratic maps.

Conclusions:

The studied Markov chain provides a model for systems with probabilistic failures.
The self-similar structure of transition operators leads to fractal spectral properties.
Connections between discrete dynamical systems and complex fractal geometry are established.