Relationship between the Mandelbrot Algorithm and the Platonic Solids

Vallières, André; Rochon, Dominic

doi:10.3390/math10030482

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…These shapes are regular polyhedral, consisting of the tetrahedron (or pyramid), cube (or hexahedron), octahedron, dodecahedron, and icosahedron. They are altogether called Platonic solid [28,29]. The traditional cuboid hotel room shape is not included in these perfect shapes.…”

Section: Platonic Solid Roommentioning

confidence: 99%

Outlandish Hospitality Quantum Marketing Based on Guest Experiences Arrangement in Irrational Architecture Hotel Room with Modules for Zero-Clean, Multi-Dimensioning, Artistic-Utilitarian Logistics and Aegean Islets Heterochronism

Zisopoulos¹,

Broni²,

Panitsidis³

et al. 2023

Preprint

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Towards Society 5.0, hospitality experiences replaced services, and Omni-Quantum marketing collects data increasing consumer selection and happiness. Our study focuses on the minimum chunk of a hotel, the guest room. We designed innovative, extravagant rooms for hotel reputation and marketing reasons. Four major room features are proposed to generate experiences. Initially, a room following zero air clean standards, full radio-magnetic, semiautomatic room fitting, and standalone zero clean bathroom. Then, the futuristic room has varying shapes, platonic solid schema, and four-dimensional emulation. Third, the room living space is full of functional and artistic components on demand. Finally, we studied an archipelago with thousands of islands as guest rooms. Hotel room reservation was the primary concern, designed as a foretaste of the following hotel overstay. Upon hotel guest arrival, the room is prepared according to customer preselection, with cleaning procedures, shape alteration, art items, advanced furniture, and expensive personalized equipment. Additional research for phobias and manias was attempted to facilitate hotel marketing working examples. Fourth, different islets/rooms target all distinct guest demands in space and time. According to Quantum marketing principles, all the above developments produce data to fulfill guest needs. Even partial implementation requires new patents and extensive funding.

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Section: Platonic Solid Roommentioning

confidence: 99%

Outlandish Hospitality Quantum Marketing Based on Guest Experiences Arrangement in Irrational Architecture Hotel Room with Modules for Zero-Clean, Multi-Dimensioning, Artistic-Utilitarian Logistics and Aegean Islets Heterochronism

Zisopoulos¹,

Broni²,

Panitsidis³

et al. 2023

Preprint

View full text Add to dashboard Cite

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On the Algebraic Foundation of the Mandelbulb

Boily

Rochon

2023

Fractals

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In this paper, we generalize the Mandelbrot set using quaternions and spherical coordinates. In particular, we use pure quaternions to define a spherical product. This product, which is inspired by the product of complex numbers, adds the angles and multiplies the radii of the spherical coordinates. We show that the algebraic structure of pure quaternions with the spherical product is a commutative unital magma. Then, we present several generalizations of the Mandelbrot set. Among them, we present a set that is visually identical to the so-called Mandelbulb. We show that this set is bounded and that it can be generated by an escape time algorithm. We also define another generalization, the bulbic Mandelbrot set. We show that one of its 2D cuts has the same dynamics as the Mandelbrot set and that we can generate this set only with a quaternionic product, without using the spherical product.

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Relationship between the Mandelbrot Algorithm and the Platonic Solids

Cited by 2 publications

References 31 publications

Outlandish Hospitality Quantum Marketing Based on Guest Experiences Arrangement in Irrational Architecture Hotel Room with Modules for Zero-Clean, Multi-Dimensioning, Artistic-Utilitarian Logistics and Aegean Islets Heterochronism

Outlandish Hospitality Quantum Marketing Based on Guest Experiences Arrangement in Irrational Architecture Hotel Room with Modules for Zero-Clean, Multi-Dimensioning, Artistic-Utilitarian Logistics and Aegean Islets Heterochronism

On the Algebraic Foundation of the Mandelbulb

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