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Your search keyword '"Julia set"' showing total 2 results
Start Over Descriptor "Julia set" Search Limiters Available in Library Collection Topic mathematical analysis Publication Year Range Last 3 years
2 results on '"Julia set"'

1. The Proof of a Conjecture Relating Catalan Numbers to an Averaged Mandelbrot-Möbius Iterated Function.

Author

Trojovský, Pavel and Venkatachalam, K.

Subjects
*ITERATIVE methods (Mathematics), *LOGICAL prediction, *COEFFICIENTS (Statistics), *BINOMIAL coefficients, *MATHEMATICAL analysis
Abstract

In 2021, Mork and Ulness studied the Mandelbrot and Julia sets for a generalization of the well-explored function hl(z) = z2 +l. Their generalization was based on the composition of hl with the Möbius transformation m(z) = 1z at each iteration step. Furthermore, they posed a conjecture providing a relation between the coefficients of (each order) iterated series of m(hl(z)) (at z = 0) and the Catalan numbers. In this paper, in particular, we prove this conjecture in a more precise (quantitative) formulation. [ABSTRACT FROM AUTHOR]

Published
2021
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2. Generation of Fractals using Polar Coordinates

Author

Serguei Charonov

Subjects
Range (mathematics), Polynomial, Fractal, Mathematical analysis, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Function (mathematics), Polar coordinate system, Mandelbrot set, Julia set, Complex number, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics
Abstract

The article describes an algorithm for generating fractals using polar coordinates. The classic Julia and Mandelbrot polynomial iteration applied to a complex number is replaced by an iteration with separate functions for distance and angle. A polynomial function is used for an angle and a power function for a distance. Varying the functions parameters allows to create a wide range of attractive pictures. Distance values ​​are used for coloring fractal images.

Published
2021

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