Invariance And Inner Fractals In Polynomial And Transcendental Fractals
A lot of formal and informal recreational study took place in the fields of Meromorphic Maps, since Mandelbrot popularized the map z <- z^2 + c. An immediate generalization of the Mandelbrot z <-z^n + c also known as the Multibrot family were also studied. In the current paper, general truncat...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
30.09.2012
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| Subjects | |
| Online Access | Get full text |
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| Summary: | A lot of formal and informal recreational study took place in the fields of
Meromorphic Maps, since Mandelbrot popularized the map z <- z^2 + c. An
immediate generalization of the Mandelbrot z <-z^n + c also known as the
Multibrot family were also studied. In the current paper, general truncated
polynomial maps of the form z <- \sum_{p>=2} a_px^p +c are studied. Two
fundamental properties of these polynomial maps are hereby presented. One of
them is the existence of shape preserving transformations on fractal images,
and another one is the existence of embedded Multibrot fractals inside a
polynomial fractal. Any transform expression with transcendental terms also
shows embedded Multibrot fractals, due to Taylor series expansion possible on
the transcendental functions. We present a method by which existence of
embedded fractals can be predicted. A gallery of images is presented alongside
to showcase the findings. |
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| DOI: | 10.48550/arxiv.1210.0228 |