An intellectual journey that began with the discovery of strange attractors derived from Chua's circuit, their translation into physical shapes by means of 3D printers, and finally, to the production of jewelry is presented. After giving the mathematical characteristics of Chua's circuit, we explain the chaotic design process, used for creating jewels, providing specifications of the used methodological approach, for its reproduction. We discuss the feasibility of this approach and the transmission of scientific contents on chaos theory, usually restricted to university students, in a high school Science, Technology, Engineering, Art, and Mathematics course, for the realization of advanced educational processes, implemented both in computational and real environments. We think that the idea of transforming science into art forms can drive students in acquiring scientific knowledge and skills, allowing them to discover the inner beauty of chaos.
REFERENCES
1.
Adamo
, A.
, Bertacchini
, P. A.
, Bilotta
, E.
, Pantano
, P.
, and Tavernise
, A.
, “Connecting art and science for education: Learning through an advanced virtual theater with ‘talking heads,’
” Leonardo
43
(5
), 442
–448
(2010
). 2.
Anishchenko
, V. S.
and Strelkova
, G. I.
, “Attractors of dynamical systems
,” in 1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No. 97TH8329)
(IEEE
, 1997
), Vol. 3, pp. 498
–503
.3.
Arneodo
, A.
, Coullet
, P.
, Peyraud
, J.
, and Tresser
, C.
, “Strange attractors in Volterra equations for species in competition
,” J. Math. Biol.
14
(2
), 153
–157
(1982
). 4.
Arneodo
, A.
, Coullet
, P.
, and Tresser
, C.
, “Possible new strange attractors with spiral structure
,” Commun. Math. Phys.
79
(4
), 573
–579
(1981
). 5.
Bertacchini
, F.
, Bilotta
, E.
, Caldarola
, F.
, and Pantano
, P.
, “The role of computer simulations in learning analytic mechanics towards chaos theory: A course experimentation
,” Int. J. Math. Educ. Sci. Technol.
50
(1
), 100
–120
(2019
). 6.
Bertacchini
, F.
, Bilotta
, E.
, Carini
, M.
, Gabriele
, L.
, Pantano
, P.
, and Tavernise
, A.
, “Learning in the smart city: A virtual and augmented museum devoted to chaos theory
,” in International Conference on Web-Based Learning
(Springer
, Berlin
, 2012b
), pp. 261
–270
.7.
Bertacchini
, F.
, Bilotta
, E.
, Demarco
, F.
, Pantano
, P.
, and Scuro
, C.
, “Multi-objective optimization and rapid prototyping for jewelry industry: Methodologies and case studies
,” Int. J. Adv. Manuf. Technol.
112
(9
), 2943
–2959
(2021
). 8.
Bertacchini
, F.
, Bilotta
, E.
, Gabriele
, L.
, Pantano
, P.
, and Servidio
, R.
, “Using Lego MindStorms in higher education: Cognitive strategies in programming a quadruped robot
,” in Workshop Proceedings of the 18th International Conference on Computers in Education, ICCE
(Asia-Pacific Society for Computers in Education, Putrajaya, Malaysia, 2010
), pp. 366
–371
.9.
Bertacchini
, F.
, Bilotta
, E.
, Gabriele
, L.
, Pantano
, P.
, and Tavernise
, A.
, “Toward the use of Chua’s circuit in education, art and interdisciplinary research: Some implementation and opportunities
,” Leonardo
46
(5
), 456
–463
(2013a
). 10.
Bertacchini
, F.
, Bilotta
, E.
, Laria
, G.
, and Pantano
, P.
, “The genesis of Chua’s circuit. Connecting science, Art and creativity
,” in Chaos, CNN, Memristors and Beyond
(World Scientific
, 2013b
), pp. 108
–123
.11.
Bertacchini
, F.
, Bilotta
, E.
, Pantano
, P.
, and Tavernise
, A.
, “Motivating the learning of science topics in secondary school: A constructivist edutainment setting for studying Chaos
,” Comput. Educ.
59
(4
), 1377
–1386
(2012a
). 12.
Bertacchini
, F.
, Scuro
, C.
, Pantano
, P.
, and Bilotta
, E.
, “A project based learning approach for improving students’ computational thinking skills
,” Front. Rob. AI
9
, 1–25 (2022
). 13.
Bilotta
, E.
, Bossio
, E.
, and Pantano
, P.
, “Chaos at school: Chua’s circuit for students in junior and senior high school
,” Int. J. Bifurc. Chaos
20
(01
), 1
–28
(2010
). 14.
Bilotta
, E.
, Di Blasi
, G.
, Stranges
, F.
, and Pantano
, P.
, “A gallery of Chua attractors: Part IV
,” Int. J. Bifurc. Chaos
17
(04
), 1017
–1077
(2007d
). 15.
Bilotta
, E.
, Di Blasi
, G.
, Stranges
, F.
, and Pantano
, P.
, “A gallery of Chua attractors: Part V
,” Int. J. Bifurc. Chaos
17
(05
), 1383
–1511
(2007e
). 16.
Bilotta
, E.
, Di Blasi
, G.
, Stranges
, F.
, and Pantano
, P.
, “A gallery of Chua attractors: Part VI
,” Int. J. Bifurc. Chaos
17
(06
), 1801
–1910
(2007f
). 17.
Bilotta
, E.
, Gervasi
, S.
, and Pantano
, P.
, “Reading complexity in Chua oscillator through music. Part I: A new way of understanding chaos
,” Int. J. Bifurc. Chaos
15
, 253
–382
(2005
). 18.
Bilotta
, E.
and Pantano
, P.
, A Gallery of Chua Attractors, A (With Dvd-rom) (Vol. 61)
(World Scientific
, 2008
).45.
Bilotta
, E.
, and Pantano
, P.
, “The language of chaos
,” Int. J. Bifurc. Chaos
16
(3
), 523
–557
(2006
).19.
Bilotta
, E.
and Pantano
, P.
, “Discrete chaotic dynamics from Chua’s oscillator: Chua machines
,” Int. J. Bifurc. Chaos
19
(01
), 1
–115
(2009
). 20.
Bilotta
, E.
, Pantano
, P.
, Cupellini
, E.
, and Rizzuti
, C.,
“Evolutionary methods for melodic sequences generation from non-linear dynamic systems
,” in Workshops on Applications of Evolutionary Computation
(Springer
, Berlin
, 2007g
), pp. 585
–592
.46.
Bilotta
, E.
, Pantano
, P.
, and Stranges
, F.
, “Computer graphics meets chaos and hyperchaos. Some key problems
,” Computers & Graphics
30
(3
), 359
–367
(2006
).21.
Bilotta
, E.
, Pantano
, P.
, and Stranges
, F.
, “A gallery of Chua attractors: Part I
,” Int. J. Bifurc. Chaos
17
(01
), 1
–60
(2007a
). 22.
Bilotta
, E.
, Pantano
, P.
, and Stranges
, F.
, “A gallery of Chua attractors: Part II
,” Int. J. Bifurc. Chaos
17
(02
), 293
–380
(2007b
). 23.
Bilotta
, E.
, Stranges
, F.
, and Pantano
, P.
, “A gallery of Chua attractors: Part III
,” Int. J. Bifurc. Chaos
17
(03
), 657
–734
(2007c
). 24.
Cai
, G.
and Huang
, J.
, “A new finance chaotic attractor
,” Int. J. Nonlinear Sci.
3
(3
), 213
–220
(2007
).25.
Chen
, H.
, “Global chaos synchronization of new chaotic systems via nonlinear control
,” Chaos Solitons Fractals
23
(4
), 1245
–1251
(2005
). 26.
Chua
, L. O.
, The Genesis of Chua’s Circuit
(Electronics Research Laboratory, College of Engineering, University of California
, Berkeley
, CA
, 1992
).27.
Chua
, L. O.
, “Chua’s circuit: An overview ten years later
,” J. Circuits, Syst. Comput.
04
(02
), 117
–159
(1994
). 47.
Chua
, L. O.
, “Global unfolding of Chua's circuit
,” IEICE Trans. Fund. Electron. Commun. Comput. Sci.
76
(5
), 704
–734
(1993
).29.
Demarco
, F.
, Bertacchini
, F.
, Scuro
, C.
, Bilotta
, E.
, and Pantano
, P.
, “Algorithms for jewelry industry 4.0
,” in International Conference on Numerical Computations: Theory and Algorithms
(Springer
, Cham
, 2019
), pp. 425
–436
.30.
Demarco
, F.
, Bertacchini
, F.
, Scuro
, C.
, Bilotta
, E.
, and Pantano
, P.
, “The development and application of an optimization tool in industrial design
,” Int. J. Interact. Des. Manuf.
14
(3
), 955
–970
(2020
). 31.
Gabriele
, L.
, Bertacchini
, F.
, Tavernise
, A.
, Vaca-Cárdenas
, L.
, Pantano
, P.
, and Bilotta
, E.
, “Lesson planning by computational thinking skills in Italian pre-service teachers
,” Inform. Educ.
18
(1
), 69
–104
(2019
). 32.
Jensen
, M. H.
, Kadanoff
, L. P.
, Libchaber
, A.
, Procaccia
, I.
, and Stavans
, J.
, “Global universality at the onset of chaos: Results of a forced Rayleigh-Bénard experiment
,” Phys. Rev. Lett.
55
(25
), 2798
(1985
). 33.
Langford
, W. F.
, “Numerical studies of torus bifurcations
,” in Numerical Methods for Bifurcation Problems
(Birkhäuser
, Basel
, 1984
), pp. 285
–295
.34.
Leipnik
, R. B.
and Newton
, T. A.
, “Double strange attractors in rigid body motion with linear feedback control
,” Phys. Lett. A
86
(2
), 63
–67
(1981
). 35.
Liu
, C.
, Liu
, T.
, Liu
, L.
, and Liu
, K.
, “A new chaotic attractor
,” Chaos Solitons Fractals
22
(5
), 1031
–1038
(2004
). 36.
Lorenz
, E. N.
, “Deterministic non-periodic flow
,” J. Atmos. Sci.
20
(2
), 130
–141
(1963
). 37.
Lorenz
, E.
, “Predictability: Does the flap of a butterfly's wing in Brazil set off a tornado in Texas?” presented at the 139th Meeting of the American Association for the Advancement of Science (1972).38.
Lü
, J.
and Chen
, G.
, “A new chaotic attractor coined
,” Int. J. Bifurc. Chaos
12
(03
), 659
–661
(2002
). 39.
Madan
, R. N.
, in Chua’s Circuit: a Paradigm for Chaos (Vol. 1)
(World Scientific
, 1993
).40.
Pan
, L.
, Zhou
, L.
, and Li
, D.
, “Synchronization of three-scroll unified chaotic system (TSUCS) and its hyper-chaotic system using active pinning control
,” Nonlinear Dyn.
73
(3
), 2059
–2071
(2013
). 41.
Poincaré
, H.
, Les méthodes nouvelles de la mécanique céleste (Vol. 3)
(Gauthier-Villars
, 1899
).48.
Qi
, G.
, Chen
, G.
, Du
, S.
, Chen
, Z.
, Yuan
, Z.
, “Analysis of a new chaotic system
,” Physica A
352
(2–4
), 295
–308
(2005
).42.
Shaw
, R.
, “Strange attractors, chaotic behavior, and information flow
,” Z. Nat. A
36
(1
), 80
–112
(1981
). 43.
Vaca-Cárdenas
, L. A.
, Bertacchini
, F.
, Tavernise
, A.
, Gabriele
, L.
, Valenti
, A.
, Olmedo
, D. E.
, and Bilotta
, E.
, “Coding with scratch: The design of an educational setting for elementary pre-service teachers
,” in 2015 International Conference on Interactive Collaborative Learning (ICL)
(IEEE
, 2015
), pp. 1171
–1177
.44.
Vaidyanathan
, S.
and Azar
, A. T.
, “Adaptive control and synchronization of Halvorsen circulant chaotic systems
,” in Advances in Chaos Theory and Intelligent Control
(Springer
, Cham
, 2016
), pp. 225
–247
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