Generation of Symmetrical Colored Images via Solution of the Inverse Problem of Chemical Reactions Discrete Chaotic Dynamics

Abstract

An automatic procedure for generating colored two-dimensional symmetrical images based on the chemical reactions discrete chaotic dynamics (CRDCD) is proposed. The inverse problem of derivation of symmetrical images from CRDCD mathematical models was formulated and solved using a special type of genetic algorithm. Different symmetrical images corresponding to the solutions of a CRDCD mathematical model for which the parameters were obtained automatically by the proposed method are presented.

Some creative properties of the 2D and 3D lattice distributed interconnected chaotic oscillators and neuronal networks

“…Chaotic regimes embedded into the different types of difference equations have been demonstrated their creative properties. Application of the presented method for creative mathematical imaging, modeling of complex, living and thinking systems and especially brain specific properties presented and discussed [1,2].…”

“…Mathematical modeling of the brain's neurons networks by interconnected oscillators with chaotic regimes is one of the effective methods to simulate brain creativity in a form of artistic images within their relation to the "brain waves" (EEG) [1,2].…”

“…Here parameter p n {X n-1 (net)} = F( , X n-1 (net)) depend from the values X n-1 (net) distributed on the lattice (net) and calculated at previous, to the considered state n, states (n-s) n, s = 1, 2,… In the simplest case X n-1 (net) just the closest to considered cell with coordinates (i,j) eight neighbors with coordinates (i-1, j-1; i+1, j; … i+1, j+1), s = 1 and F is an arbitrary chosen analytical function with parameters [1]. Computed according to (1) 2D lattice distributed sequences of 2D arrays of X n (i,j) encoded by colored palette [2]. Identical approach was applied to the Henon iterative map and to the systems of difference equations obtained from the discrete chemical reactions dynamics [1].…”

Visual Stimuli Generated by Biochemical Reactions Discrete Chaotic Dynamics as a Basis for Neurofeedback

“…According to this basic premise, an artistic image would initially appear in the brain in the form of the distributed chemical concentrations of the neurons, and the output would then be a concrete pattern created by the individual. This pattern could be visualized by the proposed mathematical model (Gontar & Grechko, 2006b).…”

“…For consistency of presentation, we repeat the description of the BRDCD mathematical model for mechanism (2) given in Gontar and Grechko (2006a, 2006b, 2007. …”