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Cyclic sequence of self-reproducing single cycles
In chemistry, a hypercycle is an abstract model of organization of self-replicating molecules connected in a cyclic, autocatalytic manner. It was introduced
Hypercycle_(chemistry)
Topics referred to by the same term
Hypercycle may refer to: Hypercycle (chemistry), a kind of reaction network prominent in a theory of the self-organization of matter Hypercycle (geometry)
Hypercycle
Type of curve in hyperbolic geometry
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight
Hypercycle_(geometry)
Type of non-Euclidean geometry
that are all the same distance from a given line lie on a curve called a hypercycle. Another special curve is the horocycle, whose normal radii (perpendicular
Hyperbolic_geometry
German biophysical chemist (1927–2019)
error threshold, error catastrophe, Eigen's paradox, and the chemical hypercycle, the cyclic linkage of reaction cycles as an explanation for the self-organization
Manfred_Eigen
System capable of producing itself
Eigen, M; Schuster, P (1977). "The hypercycle: a principle of natural self-organization. A: emergence of the hypercycle". Naturwissenschaften. 64 (11): 541–565
Autopoiesis
Curve whose normals converge asymptotically
four types: geodesics with curvature κ = 0 , {\displaystyle \kappa =0,} hypercycles with curvature 0 < | κ | < 1 , {\displaystyle 0<|\kappa |<1,} horocycles
Horocycle
Dutch musician and composer (born 1961)
(Hypercycle/Virgin, 1992) "Proze & Cons" (Hypercycle/Virgin, 1993) "Into the Light" (Hypercycle/Virgin, 1993) "Gotta Get Back (2 Love)" (Hypercycle/Virgin
Pieter_Nooten
infinite cell is an order-4 pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-4-3 pentagonal honeycomb
Order-4-3_pentagonal_honeycomb
Model of hyperbolic geometry
distinct types of generalized circles or cycles: circles, horocycles, hypercycles, and geodesics (or "hyperbolic lines"). In the Poincaré disk model, all
Poincaré_disk_model
Collection of chemical entities
Eigen, M; Schuster, P (1977). "The hypercycle: a principle of natural self-organization. A: emergence of the hypercycle". Naturwissenschaften. 64 (11): 541–565
Autocatalytic_set
Life arising from non-living matter
Peter (November 1977). "The Hypercycle. A Principle of Natural Self-Organization. Part A: Emergence of the Hypercycle" (PDF). Naturwissenschaften. 64
Abiogenesis
Abstract model for the fundamental unit of life
The chemoton is just one of several theories of life, including the hypercycle of Manfred Eigen and Peter Schuster, which includes the concept of quasispecies
Chemoton
Concept in geometry
points that are equidistant from and on one side of a given line form a hypercycle (which is a curve, not a line). Equidistant set Clapham, Christopher;
Equidistant
Lebanese businessman
the Class of 2024". Haigazian University. 11 June 2024. "About HyperCycle.ai". HyperCycle.ai. 9 June 2023. "زياد حايك يُعلن ترشّحه لرئاسة الجمهورية: درب
Ziad_Hayek
Characterizes spherical triangles with fixed base and area
also be proven for hyperbolic triangles, for which the apex lies on a hypercycle. Given a fixed base A B , {\displaystyle AB,} an arc of a great circle
Lexell's_theorem
infinite cell consists of a hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-6-3_square_honeycomb
infinite cell consists of a pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-5-3_square_honeycomb
Model of hyperbolic geometry
not distorted. All other circles are distorted, as are horocycles and hypercycles. Chords that meet on the boundary circle are limiting parallel lines
Beltrami–Klein_model
infinite cell consists of an octagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-8-3 triangular honeycomb
Order-8-3_triangular_honeycomb
American theoretical biologist
Eigen, M; Schuster, P (1977). "The hypercycle: a principle of natural self-organization. A: emergence of the hypercycle". Naturwissenschaften. 64 (11): 541–565
Robert_Rosen_(biologist)
infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-7-3 triangular honeycomb
Order-7-3_triangular_honeycomb
American motorcycle racer (born 1969)
Attack Suzuki. 1997 - Won the 750 Supersport class championship riding for Hypercycle Suzuki. 1996 - Six top-five finishes in 600 SuperSport, Five top-10 750cc
Jason_Pridmore
infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-3-6 heptagonal honeycomb
Order-3-6_heptagonal_honeycomb
infinite cell consists of a pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-4-4 pentagonal honeycomb
Order-4-4_pentagonal_honeycomb
infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-3-5 heptagonal honeycomb
Order-3-5_heptagonal_honeycomb
Proposed alternative scenarios related to abiogenesis
between the molecular chaos and a self-replicating hypercycle in a prebiotic soup. In a hypercycle, the information storing system (possibly RNA) produces
Alternative abiogenesis scenarios
Alternative_abiogenesis_scenarios
Upper-half plane model of hyperbolic non-Euclidean geometry
projection of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles
Poincaré_half-plane_model
American motorcycle racer
Championship Position: First Place (2002) Team(s): American Honda, Erion Honda, HyperCycle Suzuki Motorcycle(s): Honda CBR600F3, Honda CBR600F4, Suzuki GSX-R600
Nicky_Hayden
hyperbolic Laguerre transformations that map a circle to a horocycle to a hypercycle and converge towards a line. This uses the split-complex numbers.
Laguerre_transformations
Equation for radii of tangent circles
for mutually tangent configurations in hyperbolic geometry including hypercycles and horocycles, if k j {\displaystyle k_{j}} is the geodesic curvature
Descartes'_theorem
Distance from one geometric object to another along a line perpendicular to both
surface fitting and for defining offset surfaces. Distance between sets Hypercycle (geometry) Moment of inertia Signed distance Ballantine, J. P.; Jerbert
Perpendicular_distance
All Latin and Greek roots beginning with G
epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid, isocyclic, mesocyclone, monocyclic, polycyclic, pseudocyclosis
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
Polyhedron with regular congruent polygons as faces
honeycomb {7,3,3}; they are inscribed in an equidistant surface (a 2-hypercycle), which has two ideal points. Another group of regular polyhedra comprise
Regular_polyhedron
Hypersurface in hyperbolic space
curvature were any less, the surface would be an (N − 1)-dimensional hypercycle. Roberto Bonola (1906), Non-Euclidean Geometry, translated by H.S. Carslaw
Horosphere
Process of forming order by local interactions
Networks, Wiley & Sons. Manfred Eigen and Peter Schuster (1979), The Hypercycle: A principle of natural self-organization, Springer. Myrna Estep (2003)
Self-organization
infinite cell consists of a heptagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli
Order-3-4 heptagonal honeycomb
Order-3-4_heptagonal_honeycomb
the Euclidean plane, with the vertices circumscribed by horocycles or hypercycles rather than circles. Regular apeirogons that are scaled to converge at
List_of_regular_polytopes
Fundamental result in geometry
counterpart: instead of circles, the level sets become pairs of curves called hypercycles, and the foliation is non-singular. In Taxicab Geometry, a type of non-Euclidean
Sum_of_angles_of_a_triangle
honeycomb. The order-4 hexagonal tiling honeycomb contains , which tile 2-hypercycle surfaces and are similar to the truncated infinite-order triangular tiling
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
All Latin and Greek roots beginning with C
epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid, isocyclic, mesocyclone, monocyclic, polycyclic, pseudocyclosis
List of Greek and Latin roots in English/C
List_of_Greek_and_Latin_roots_in_English/C
Triangle in hyperbolic geometry
circumscribed circle (see below). Its vertices can lie on a horocycle or hypercycle. Hyperbolic triangles have some properties that are analogous to those
Hyperbolic_triangle
Hungarian biologist
major transitions in evolution. a discussion on the confusion between hypercycle and collectively autocatalytic system (link) Apart from the aforementioned
Eörs_Szathmáry
1994 French TV series or program
inductance rope. He has several vehicles, including a nimble airborne Hypercycle, a cloaking multi-passenger cruiser, and an upgraded 1999 Mustang named
Phantom_2040
pairs of ultraparallel mirrors: . This honeycomb contains that tile 2-hypercycle surfaces, which are similar to the paracompact order-3 apeirogonal tiling
Square_tiling_honeycomb
Emergence of a higher level of organization or control through evolution
independent components, such as molecules (as theorized for instance by hypercycles), cells, or individuals, and the emergence of a system steering or controlling
Metasystem_transition
boundary. Lines parallel to the boundaries of the band within the band are hypercycles whose common axis is the line through the middle of the band. Mercator
Band_model
Musical artist
ISBN 978-0-00-748961-9. Mic (7 March 2011). "Post-(Clan of) XYMOX – Vaselyn, Hypercycle, Born for Bliss (Biography Part 5/5)". Unruhr. Retrieved 3 August 2011
Anka_Wolbert
American economist
introduced by Rosser in 1991 (Chap. 12). It involves combining the idea of the hypercycle, an idea due to Manfred Eigen and Peter Schuster (1979), with that of
J._Barkley_Rosser_Jr.
1959 woodcut by M. C. Escher
equilateral triangles, as the figure depicts. Rather, the white curves are hypercycles that meet the boundary circle at angles of cos−1 21/4 − 2−1/4/2, approximately 80°
Circle_Limit_III
German-Iranian philosopher of medicine
subsystem of a hybrid hypercycle of two evolving partners, biosphere and technosphere, which due to the enormous dynamics of the hypercycle rapidly coevolve
Kazem_Sadegh-Zadeh
Programming paradigm
inner-services within a composite service run in a parallel burst called a "hypercycle". This is one of the means by which automatic parallel-processing is supported
Service-oriented_programming
Scientific study of chemical processes involving metabolites
inputs to other chemical reactions. Such systems have been described as hypercycles.[citation needed] Metabonomics is defined as "the quantitative measurement
Metabolomics
Darwinian evolution of self-replicating entities within framework of physical chemistry
Springer. p. 1. ISBN 978-3-540-26395-1. Eigen M, Schuster P (1979). The Hypercycle: A Principle of Natural Self-Organization. Berlin: Springer-Verlag.
Quasispecies_model
domain, [((3,∞,3)),((3,∞,3))]: . This honeycomb contains and that tile 2-hypercycle surfaces, which are similar to the paracompact infinite-order triangular
Order-4_octahedral_honeycomb
Mexican researcher
(UAM), Mexico. His thesis subject was Reductionism and Emergentism in the Hypercycle Theory (Reduccionismo y emergentismo en la teoría del hiperciclo). Rubio
Julio_E._Rubio
Dutch biophysicist
field of pre-biotic study: Spiral wave structure in pre-biotic evolution hypercycle stable against parasites. In 1991, Hogeweg became a full professor of
Paulien_Hogeweg
com/losinggeneration Hypercycles Archived 2017-03-28 at the Wayback Machine on freegamedev.net hypercycles on github.com Gravier, Jean (2021-03-17), jevarg/hypercycles, retrieved
List of commercial video games with later released source code
List_of_commercial_video_games_with_later_released_source_code
Uniform tiling of the hyperbolic plane
angle at each vertex, while in Escher's woodcut they appear to be smooth hypercycles. Circle Limit III Square tiling Uniform tilings in hyperbolic plane List
Alternated_octagonal_tiling
Isometric automorphisms of a hyperbolic space
perpendicular to the given line; points off the given line move along hypercycles; three degrees of freedom. Orientation reversing reflection through a
Hyperbolic_motion
and with all vertices on the ideal surface. It contains and that tile 2-hypercycle surfaces, which are similar to these paracompact order-4 apeirogonal tilings
Order-4 square tiling honeycomb
Order-4_square_tiling_honeycomb
Study of geometries as axiomatic systems
in Euclidean geometry, but don't in hyperbolic geometry (they form a hypercycle.) Advocates of the position that Euclidean geometry is the one and only
Foundations_of_geometry
Population structure of viruses with a large number of variant genomes
Schuster P (November 1977). "The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle". Die Naturwissenschaften. 64
Viral_quasispecies
for hyperbolic constructions. A hypercompass can be used to construct a hypercycle given the central line and radius. A horocompass can be used to construct
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Category of coordinate systems
quadrilateral). Also in hyperbolic geometry there are no equidistant lines (see hypercycles). This all has influences on the coordinate systems. There are however
Coordinate systems for the hyperbolic plane
Coordinate_systems_for_the_hyperbolic_plane
Long-term change in dominant economic activity
Fig. 1. Nested hypercycles of the transformations through the parallel evolution of four forms of capital
Transformation_in_economics
and with all vertices on the ideal surface. It contains and that tile 2-hypercycle surfaces, which are similar to the paracompact tilings and (the truncated
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
HYPERCYCLE
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Girl/Female
Indian
Sea
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi
A Name in Sanskrit Classics
Male
Welsh
Variant spelling of Welsh Meuric, MEURIG means "dark-skinned; Moor."
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Blossom; A Creeper of Love
Surname or Lastname
English
English : variant spelling of Sayer.
Boy/Male
British, English
Laurel
Girl/Female
Christian & English(British/American/Australian)
Spirited in Battle
Boy/Male
Hindu, Indian, Tamil
Lord Muruga; Lord Vishnu; God with 6 Faces (Subrahmanyeswara Swamy)
Female
English
Pet form of English Vanessa, possibly NESSIE means "to appear."
Boy/Male
Buddhist, Indian
One Mountain
HYPERCYCLE
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HYPERCYCLE
HYPERCYCLE
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