One more look on visualization of operation of a root-finding algorithm

Abstract

Many algorithms that iteratively find solution of an equation require tuning. Due to the complex dependence of many algorithm’s elements, it is difficult to know their impact on the work of the algorithm. The article presents a simple root-finding algorithm with self-adaptation that requires tuning, similarly to evolutionary algorithms. Moreover, the use of various iteration processes instead of the standard Picard iteration is presented. In the algorithm’s analysis, visualizations of the dynamics were used. The conducted experiments and the discussion regarding their results allow to understand the influence of tuning on the proposed algorithm. The understanding of the tuning mechanisms can be helpful in using other evolutionary algorithms. Moreover, the presented visualizations show intriguing patterns of potential artistic applications.

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

“…The conducted research serves to visualise the impact of the proposed algorithm modifications on the behaviour of the particle. They allow conducting not only the discussion on the behaviour of a particle, but also to present images of aesthetic character and artistic meaning [ 31 , 32 ].…”