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Advances in Intelligent Systems and Computing, vol.

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In the paper, a modification of rendering algorithm of polynomiograph is presented. Polynomiography is a method of visualization of complex polynomial root finding process and it has applications among other things in aesthetic wybrane wzory matematyczne generation.

The proposed modification is based on a perturbation mapping, which is added in the iteration process of the root finding method. The use of the perturbation mapping alters the shape of the polynomiograph, obtaining in this way new and diverse patterns.

The results from the paper can further enrich the functionality of wybrane wzory matematyczne existing polynomiography software.

Abstract and Applied Analysis, wybrane wzory matematyczne. In this paper a survey of some modifications based on the classic Newton's and the higher order Newton-like root finding methods for complex polynomials are presented.

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Instead of the standard Picard's iteration several different iteration processes, described in the literature, that we call as non-standard ones, are used.

Kalantari's visualizations of root finding process are interesting from at least three points of view: By combining different kinds of iterations, different convergence tests, and different colouring we obtain a great variety of wybrane wzory matematyczne.


We also check experimentally that using complex parameters instead of real wybrane wzory matematyczne in multi-parameter iterations do not destabilize the iteration process. Moreover, we obtain nicely looking polynomiographs that are interesting from the artistic point of view.

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Real parts of the parameters alter symmetry, whereas imaginary ones cause asymmetric twisting of wybrane wzory matematyczne. Fractals 22 4, 7 pages, Abstract. In the paper, we generalized the idea of circle inversion to star-shaped sets and used the generalized inversion to replace the circle inversion transformation in the algorithm for the generation of the circle inversion wybrane wzory matematyczne.

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In this way, wybrane wzory matematyczne obtained the star-shaped set inversion fractals. The examples that we have presented show that we were able to obtain very diverse fractal patterns by using the proposed extension and that these patterns are different from those obtained with the circle inversion method.

Moreover, because circles are star-shaped sets, the proposed generalization allows us to deform the circle wybrane wzory matematyczne fractals in a very easy and intuitive way. Polynomiography is a method of visualization of complex polynomial root finding process.


One of the applications of polynomiography is wybrane wzory matematyczne of aesthetic patterns. In this paper, we present two new algorithms for polynomiograph rendering that allow to obtain new diverse patterns.

The algorithms are based on the ideas used to render the well known Mandelbrot and Julia sets.

The results obtained with the proposed algorithms can enrich the functionality of the existing polynomiography software. In the paper visualizations of wybrane wzory matematyczne modifications based on the Newton's root finding of complex polynomials are presented.

Instead of the standard Picard iteration several different iterative processes described in the literature, that we call as wybrane wzory matematyczne ones, are used.

Following Kalantari such visualizations are called polynomiographs.

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