Multifractal spectrum of an experimental (video feedback) Farey Tree

A camera films a screen to which it is connected. It films its own image, feeding back the image to the screen. The camera can turn around an optical axis. A pattern of p light spots on the screen and q turns (feedback loops) of the camera appears, where p and q follow the hierarchy of a Farey tree....

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Detalles Bibliográficos
Autores principales: Piacquadio, M., Rosen, M.
Formato: JOUR
Materias:
Farey-tree
Hausdorff measure
Multifractality
Number theory
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00224715_v127_n4_p783_Piacquadio
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00224715_v127_n4_p783_Piacquadio
record_format dspace
spelling todo:paper_00224715_v127_n4_p783_Piacquadio2023-10-03T14:32:56Z Multifractal spectrum of an experimental (video feedback) Farey Tree Piacquadio, M. Rosen, M. Farey-tree Hausdorff measure Multifractality Number theory A camera films a screen to which it is connected. It films its own image, feeding back the image to the screen. The camera can turn around an optical axis. A pattern of p light spots on the screen and q turns (feedback loops) of the camera appears, where p and q follow the hierarchy of a Farey tree. The Farey tree induces a measure distribution μ on the unit segment, different from the hyperbolic one μ H induced by the Farey-Brocot interpolation. In this paper the multifractal spectrum of μ is studied and compared with that of μ H ; the study of the latter spectrum is refined. The spectra are studied in this paper by means of different tools from Number Theory. The results of this study are interpreted in terms of p and q, empirically obtained in the video feedback experiment. © Springer Science+Business Media, LLC 2007. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00224715_v127_n4_p783_Piacquadio
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Farey-tree
Hausdorff measure
Multifractality
Number theory
spellingShingle Farey-tree
Hausdorff measure
Multifractality
Number theory
Piacquadio, M.
Rosen, M.
Multifractal spectrum of an experimental (video feedback) Farey Tree
topic_facet Farey-tree
Hausdorff measure
Multifractality
Number theory
description A camera films a screen to which it is connected. It films its own image, feeding back the image to the screen. The camera can turn around an optical axis. A pattern of p light spots on the screen and q turns (feedback loops) of the camera appears, where p and q follow the hierarchy of a Farey tree. The Farey tree induces a measure distribution μ on the unit segment, different from the hyperbolic one μ H induced by the Farey-Brocot interpolation. In this paper the multifractal spectrum of μ is studied and compared with that of μ H ; the study of the latter spectrum is refined. The spectra are studied in this paper by means of different tools from Number Theory. The results of this study are interpreted in terms of p and q, empirically obtained in the video feedback experiment. © Springer Science+Business Media, LLC 2007.
format JOUR
author Piacquadio, M.
Rosen, M.
author_facet Piacquadio, M.
Rosen, M.
author_sort Piacquadio, M.
title Multifractal spectrum of an experimental (video feedback) Farey Tree
title_short Multifractal spectrum of an experimental (video feedback) Farey Tree
title_full Multifractal spectrum of an experimental (video feedback) Farey Tree
title_fullStr Multifractal spectrum of an experimental (video feedback) Farey Tree
title_full_unstemmed Multifractal spectrum of an experimental (video feedback) Farey Tree
title_sort multifractal spectrum of an experimental (video feedback) farey tree
url http://hdl.handle.net/20.500.12110/paper_00224715_v127_n4_p783_Piacquadio
work_keys_str_mv AT piacquadiom multifractalspectrumofanexperimentalvideofeedbackfareytree
AT rosenm multifractalspectrumofanexperimentalvideofeedbackfareytree
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