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Complexity and nonlinearity of colloid electrical transducers

Raphael Fortulan, Noushin Raeisi Kheirabadi, Alessandro Chiolerio, Andrew Adamatzky

Abstract

This work explores the complexity and nonlinearity of seven different colloidal suspensions-Au, ferrofluid, TiO2}, ZnO, g-C3N4, MXene, and PEDOT:PSS-when electrically stimulated with fractal, chaotic, and random binary signals. The recorded electrical responses were analyzed using entropy, file compression, fractal dimension, and Fisher information measures to quantify complexity. The nonlinearity introduced by each colloid was evaluated by the deviation of the output from the best-fit hyperplane of the input-output mapping. The results showed that TiO2 was the most complex colloid across all inputs, exhibiting high entropy, poor compressibility, and an unpredictable response pattern. The colloids also exhibited significant nonlinearity, making them promising candidates for reservoir computation, where the mapping of inputs into high-dimensional nonlinear states is advantageous. This study provides insight into the dynamics of colloids and their potential for unconventional computational applications that exploit their inherent complexity and nonlinearity, and it provides a rapid method for assessing the suitability of a particular material for use as a computational substrate before others.

Complexity and nonlinearity of colloid electrical transducers

Abstract

This work explores the complexity and nonlinearity of seven different colloidal suspensions-Au, ferrofluid, TiO2}, ZnO, g-C3N4, MXene, and PEDOT:PSS-when electrically stimulated with fractal, chaotic, and random binary signals. The recorded electrical responses were analyzed using entropy, file compression, fractal dimension, and Fisher information measures to quantify complexity. The nonlinearity introduced by each colloid was evaluated by the deviation of the output from the best-fit hyperplane of the input-output mapping. The results showed that TiO2 was the most complex colloid across all inputs, exhibiting high entropy, poor compressibility, and an unpredictable response pattern. The colloids also exhibited significant nonlinearity, making them promising candidates for reservoir computation, where the mapping of inputs into high-dimensional nonlinear states is advantageous. This study provides insight into the dynamics of colloids and their potential for unconventional computational applications that exploit their inherent complexity and nonlinearity, and it provides a rapid method for assessing the suitability of a particular material for use as a computational substrate before others.

Paper Structure

This paper contains 9 sections, 4 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Materials Fabrication
  3. Experimental setup
  4. Koch snowflake
  5. Lorenz system
  6. Random Bombardment
  7. Black-Box Complexity
  8. Black-box Nonlinearity
  9. Conclusions

Figures (2)

  • Figure 1: Measured electrical responses of the colloids for random, chaotic, and fractal signal inputs.
  • Figure 2: (a) Measured electrical response for a chaotic signal for the TiO2 colloid. The inset shows a zoomed-in region of the curve to elucidate the complex and unpredictable pattern exhibited by the colloid when subjected to electrical signals. (b) Frequency-time wavelet spectrogram of the measured electrical response for a chaotic signal for the TiO2 colloid. The predominantly dark plot with limited areas of light shading indicates a wide distribution of frequencies over time and a non-repetitive pattern in the data.