On computational complexity of Siegel Julia sets

I. Binder; M. Braverman; M. Yampolsky

doi:10.1007/s00220-006-1546-3

On computational complexity of Siegel Julia sets

I. Binder, M. Braverman, M. Yampolsky

Research output: Contribution to journal › Review article › peer-review

9 Scopus citations

Abstract

It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

Original language	English (US)
Pages (from-to)	317-334
Number of pages	18
Journal	Communications In Mathematical Physics
Volume	264
Issue number	2
DOIs	https://doi.org/10.1007/s00220-006-1546-3
State	Published - Jun 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-006-1546-3

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title = "On computational complexity of Siegel Julia sets",

abstract = "It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.",

author = "I. Binder and M. Braverman and M. Yampolsky",

year = "2006",

month = jun,

doi = "10.1007/s00220-006-1546-3",

language = "English (US)",

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journal = "Communications In Mathematical Physics",

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T1 - On computational complexity of Siegel Julia sets

AU - Binder, I.

AU - Braverman, M.

AU - Yampolsky, M.

PY - 2006/6

Y1 - 2006/6

N2 - It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

AB - It has been previously shown by two of the authors that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

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UR - http://www.scopus.com/inward/citedby.url?scp=33645969590&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-1546-3

DO - 10.1007/s00220-006-1546-3

M3 - Review article

AN - SCOPUS:33645969590

SN - 0010-3616

VL - 264

SP - 317

EP - 334

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -

On computational complexity of Siegel Julia sets

Abstract

All Science Journal Classification (ASJC) codes

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