Fractality in resistive circuits: the Fibonacci resistor networks
We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network’s equivalent resistance conve...
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| Veröffentlicht in: | The European physical journal. B, Condensed matter physics Condensed matter physics, 2024-08, Vol.97 (8), Article 121 |
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| container_title | The European physical journal. B, Condensed matter physics |
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| creator | dos Anjos, Petrus H. R. Oliveira, Fernando A. Azevedo, David L. |
| description | We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network’s equivalent resistance converges uniformly in the parameter
α
=
r
2
r
1
∈
[
0
,
+
∞
)
, where
r
1
and
r
2
are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.
Graphical abstract |
| doi_str_mv | 10.1140/epjb/s10051-024-00750-z |
| format | Article |
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α
=
r
2
r
1
∈
[
0
,
+
∞
)
, where
r
1
and
r
2
are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.
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α
=
r
2
r
1
∈
[
0
,
+
∞
)
, where
r
1
and
r
2
are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.
Graphical abstract</description><subject>Combinatorial analysis</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Fibonacci numbers</subject><subject>Fluid- and Aerodynamics</subject><subject>Networks</subject><subject>New Trends in Statistical Physics of Complex Systems: Theoretical and Experimental Approaches</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Resistors</subject><subject>Scale invariance</subject><subject>Self-similarity</subject><subject>Sequences</subject><subject>Solid State Physics</subject><subject>Topical Review - Statistical and Nonlinear Physics</subject><issn>1434-6028</issn><issn>1434-6036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNqFkMFOwzAMhiMEEmPwDFTiHOa0TtNymyYGSJO47B6lqQsZox1JBtqeno5OcORkH_7vt_Uxdi3gVgiECW1W1SQIACk4pMgBlAS-P2EjgRnyHLL89HdPi3N2EcIKAEQucMSmc29sNGsXd4lrE0_Bheg-KbHO262L4S6Jr5TMXdW1xlp3THQ-aSl-df4tXLKzxqwDXR3nmC3n98vZI188PzzNpgtuUwGRIwGCrG1d15VILWIpMmMQZUMIDSIUyvQ_KbKysKRMClWdYylrowSURTZmN0PtxncfWwpRr7qtb_uLOoMyLVCVuexTakhZ34XgqdEb796N32kB-qBLH3TpQZfudekfXXrfk8VAhp5oX8j_9f-HfgPpInHV</recordid><startdate>20240801</startdate><enddate>20240801</enddate><creator>dos Anjos, Petrus H. R.</creator><creator>Oliveira, Fernando A.</creator><creator>Azevedo, David L.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3456-554X</orcidid></search><sort><creationdate>20240801</creationdate><title>Fractality in resistive circuits: the Fibonacci resistor networks</title><author>dos Anjos, Petrus H. R. ; Oliveira, Fernando A. ; Azevedo, David L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c210t-4e0405dcdddb12c44913aa445fe40f44087a0167ec58ce7a20bd6495da710983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorial analysis</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Fibonacci numbers</topic><topic>Fluid- and Aerodynamics</topic><topic>Networks</topic><topic>New Trends in Statistical Physics of Complex Systems: Theoretical and Experimental Approaches</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Resistors</topic><topic>Scale invariance</topic><topic>Self-similarity</topic><topic>Sequences</topic><topic>Solid State Physics</topic><topic>Topical Review - Statistical and Nonlinear Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>dos Anjos, Petrus H. R.</creatorcontrib><creatorcontrib>Oliveira, Fernando A.</creatorcontrib><creatorcontrib>Azevedo, David L.</creatorcontrib><collection>CrossRef</collection><jtitle>The European physical journal. B, Condensed matter physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>dos Anjos, Petrus H. R.</au><au>Oliveira, Fernando A.</au><au>Azevedo, David L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractality in resistive circuits: the Fibonacci resistor networks</atitle><jtitle>The European physical journal. B, Condensed matter physics</jtitle><stitle>Eur. Phys. J. B</stitle><date>2024-08-01</date><risdate>2024</risdate><volume>97</volume><issue>8</issue><artnum>121</artnum><issn>1434-6028</issn><eissn>1434-6036</eissn><abstract>We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network’s equivalent resistance converges uniformly in the parameter
α
=
r
2
r
1
∈
[
0
,
+
∞
)
, where
r
1
and
r
2
are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.
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| subjects | Combinatorial analysis Complex Systems Condensed Matter Physics Fibonacci numbers Fluid- and Aerodynamics Networks New Trends in Statistical Physics of Complex Systems: Theoretical and Experimental Approaches Physics Physics and Astronomy Resistors Scale invariance Self-similarity Sequences Solid State Physics Topical Review - Statistical and Nonlinear Physics |
| title | Fractality in resistive circuits: the Fibonacci resistor networks |
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