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Whole of an object being mathematically similar to part of itself
show self-similarity under arbitrary magnification, it is impossible to recreate this physically. Peitgen et al. suggest studying self-similarity using
Self-similarity
Counterintuitive observation
Coast of Britain? Statistical Self-Similarity and Fractional Dimension", published on 5 May 1967, Mandelbrot discusses self-similar curves that have Hausdorff
Coastline_paradox
Property of objects which are scaled or mirrored versions of each other
function for different bases Logarithmic spirals are self-similar A similarity (also called a similarity transformation or similitude) of a Euclidean space
Similarity_(geometry)
In data analysis, the self-similarity matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different
Self-similarity_matrix
Continuous function that is not absolutely continuous
found in the article on de Rham curves. Other fractals possessing self-similarity are described with other kinds of monoids. The dyadic monoid is itself
Cantor_function
Infinitely detailed mathematical structure
exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication
Fractal
Self-similar processes are stochastic processes satisfying a mathematically precise version of the self-similarity property. Several related properties
Self-similar_process
Fractal named after mathematician Benoit Mandelbrot
587L. doi:10.1007/bf02098448. S2CID 122439436. J. Milnor (1989). "Self-Similarity and Hairiness in the Mandelbrot Set". In M. C. Tangora (ed.). Computers
Mandelbrot_set
Concept in partial differential equations
{\text{erf}}(\cdot )} is the error function. Gratton, J. (1991). Similarity and self similarity in fluid dynamics. Fundamentals of Cosmic Physics. Vol. 15.
Self-similar_solution
Real-valued function that quantifies similarity between two objects
related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects
Similarity_measure
Integer sequence
sequence, the sequence of its exponents, and the Thue–Morse sequence are all self-similar: they have the property that the subsequence of values at even positions
Gould's_sequence
Real-valued number of spatial dimensions
brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity, where he discusses fractional dimensions. In that paper, Mandelbrot
Fractal_dimension
Set of points on a line segment with certain topological properties
Cantor set is equal to the union of two functions, the left and right self-similarity transformations of itself, T L ( x ) = x / 3 {\displaystyle T_{L}(x)=x/3}
Cantor_set
Fractal which resembles a plant
provide models for certain plants, leaves, and ferns, by virtue of the self-similarity which often occurs in branching structures in nature. But nature also
Barnsley_fern
Similarity measure for number sequences
analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of
Cosine_similarity
Invariant measure of fractal dimension
objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have
Hausdorff_dimension
In computer networks, self-similarity is a feature of network data transfer dynamics. When modeling network data dynamics the traditional time series
Self-Similarity of Network Data Analysis
Self-Similarity_of_Network_Data_Analysis
Regularity in sensory qualia or abstract ideas
shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coastlines and
Pattern
Family of three random counting measures
{\displaystyle \psi _{\theta }} of K {\displaystyle K} encodes a distributional self-similarity property whereby all counts in restrictions (thinnings) to subspaces
Poisson-type_random_measure
Features that do not change if length or energy scales are multiplied by a common factor
invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of
Scale_invariance
Self-similar growth curve
shape is unaltered with each successive curve, a property known as self-similarity. Possibly as a result of this unique property, the spira mirabilis
Logarithmic_spiral
Graphical plot
identifying regions of close similarity after sequence alignment. It is a type of recurrence plot. One way to visualize the similarity between two protein or
Dot_plot_(bioinformatics)
Increase in size of a material's crystallites at high temperature
Hillert's self-similar solution. Hence a search for a new possible self-similar solution was initiated that indeed led to a new class of self-similar distribution
Grain_growth
French-American mathematician (1924–2010)
the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature. In 1936, at the age of 11, Mandelbrot and his family emigrated
Benoit_Mandelbrot
Field of mathematics and science based on non-linear systems and initial conditions
patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle
Chaos_theory
Mathematical curve whose shape is a fractal
others have studied self-similarity of fractal curves, and have applied theory of fractals to modelling natural phenomena. Self-similarity occurs, and analysis
Fractal_curve
Probability theory concept
order fractional Brownian motion, abbreviated as n-fBm. n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order n are stationary
Fractional_Brownian_motion
Fractal set
with interesting properties, such as periodic tiling of the plane and self-similarity in three homothetic parts. The infinite tribonacci word is a word constructed
Rauzy_fractal
Type of social learning
learning biases are the conformity bias, success bias, prestige bias and self-similarity biases, which will be explained in greater detail. A study by Clegg
Imitative_learning
Latin phrase meaning 'continuing forever'
" The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem On Poetry: a Rhapsody
Ad_infinitum
seem that the small-world networks are not self-similar under a length-scale transformation. Self-similarity has been discovered in the solvent-accessible
Fractal_dimension_on_networks
Vegetable, member of the cabbage family
(407): 109–114. doi:10.17660/ActaHortic.1996.407.12. Fractal Food: Self-Similarity on the Supermarket Shelf (John Walker, March 2005) Procedural fractal
Romanesco_broccoli
Fractal curve resembling a blancmange pudding
This integral is also self-similar on the unit interval, under an action of the dyadic monoid described in the section Self similarity. Here, the representation
Blancmange_curve
Study of the attraction between people that leads to friendship or romance
attraction-similarity model (2007), there is a lay belief that people with actual similarity produce initial attraction. The perceived similarity is either self-serving
Interpersonal_attraction
scaling) is a litmus test that shows whether an evolving system exhibits self-similarity. In general a function is said to exhibit dynamic scaling if it satisfies:
Dynamic_scaling
derived from a bisected, self-similar landscape and a community-level probability rule. However, Maddux showed that this self-similarity model generates biologically
Occupancy frequency distribution
Occupancy_frequency_distribution
Model of cultural evolution
groups according to how quick "opinion leaders" adopt them. Meanwhile, self-similarity transmission is the tendency to copy those individuals who are similar
Cultural_group_selection
Similarity is one of the three essential conditions (Geometric Similarity, Dynamic Similarity and Kinematic Similarity) to complete the similarities between
Kinematic_similarity
Antenna with a fractal shape
that self-similarity was the requirement to make antennas frequency and bandwidth invariant. Angle-defined antennas are self-similar, but other self-similar
Fractal_antenna
Energy transfer between scales of motion
inertial subrange. The dynamics at these scales is described by use of self-similarity, or by assumptions – for turbulence closure – on the statistical properties
Energy_cascade
Design method of discrete wavelet transforms
satisfies certain self-similarity relations in time-space and scale-frequency, as well as completeness and regularity relations. Self-similarity in time demands
Multiresolution_analysis
Self-similar fractal curve
French mathematician Paul Lévy, who was the first to describe its self-similarity properties as well as to provide a geometrical construction showing
Lévy_C_curve
Forensic technique to validate audio recordings
by ambiguity based on fixed frequency offsets during recording, and self-similarity within the mains frequency database, particularly for recordings shorter
Electrical network frequency analysis
Electrical_network_frequency_analysis
Rectangle with side lengths in the golden ratio
times longer than another. Golden rectangles exhibit a special form of self-similarity: if a square is added to the long side, or removed from the short side
Golden_rectangle
Method for the construction of fractals
provide models for certain plants, leaves, and ferns, by virtue of the self-similarity which often occurs in branching structures in nature. — Michael Barnsley
Iterated_function_system
Motion characterized by chaotic changes in pressure and flow velocity
the concept of self-similarity. As a result, the Kolmogorov microscales were named after him. It is now known that the self-similarity is broken so the
Turbulence
Concept in theoretical physics
invariance and conformal invariance, symmetries in which a system exhibits self-similarity; in some cases, the parameters of the model can be assigned to special
Renormalization_group
1500 self-portrait by Albrecht Dürer
not to be self-portraits, they are not named as such, artist historians believe that since they bear remarkable similarities to his known self-portraits—including
Self-Portrait_(Dürer,_Munich)
measured traffic traces have led to the wide recognition of self-similarity in network traffic. Self-similar Ethernet traffic exhibits dependencies over a long
Long-tail_traffic
Field of knowledge
wave crests does not change one's view of the sea. Fractals possess self-similarity. Popular mathematics is the act of presenting mathematics without technical
Mathematics
Synonym of phonon
translational symmetry to the potential in a Schrödinger equation. Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational
Fracton
Stochastically generated naturalistic terrain
behavior. Many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces. Moreover, variations in surface
Fractal_landscape
Vehicle operated with reduced or no human input on public roads
A self-driving car, also known as an autonomous car, driverless car, robotic car, or robo-car, is a car that is capable of operating with reduced or no
Self-driving_car
Self-similar solution describing the fluid dynamics of explosions
within the shock sphere must be equal to E {\displaystyle E} . Due to self-similarity, it is clear that not only the total energy within a sphere of radius
Taylor–von Neumann–Sedov blast wave
Taylor–von_Neumann–Sedov_blast_wave
dissimilarity Jensen–Shannon divergence Self-similarity Similarity measure Variance Wolpert, David H.; Macready, William (2004). "Self-dissimilarity as a high dimensional
Self-dissimilarity
Mandelbar Set
repeats with variations at different scales, showing the same sort of self-similarity as the Mandelbrot set. In addition to smaller tricorns, smaller versions
Tricorn_(mathematics)
Behavioral effect in virtual worlds
harmed. From these results, the authors proposed avatar self-similarity as a "middle ground between self-perception and priming-oriented explanations". Studies
Proteus_effect
Recursive visual effect
Infinite regress Infinity mirror Matryoshka doll Quine Scale invariance Self-similarity Story within a story § Fractal fiction Video feedback Johannes (Jan)
Droste_effect
Inherent structure of the mandelbrot set
tests in the field of "Julia set" theory. Pickover's biomorphs show a self-similarity at different scales, a common feature of dynamical systems with feedback
Pickover_stalk
Repeated basic operation in a cryptosystem
from the key schedule. Parameterization is essential to reduce the self-similarity of the cipher, which could lead to slide attacks. Increasing the number
Round_(cryptography)
2002 book on fractal geometry
called Möbius transformations, and their connections with symmetry and self-similarity. These patterns were glimpsed by German mathematician Felix Klein,
Indra's_Pearls_(book)
Russian nested wooden toy
portal Toys portal Chinese boxes Droste effect Fractal Mise en abyme Self-similarity Shaker-style pantry box Stacking (video game) Turducken Turtles all
Matryoshka_doll
One's internal beliefs about oneself
In the psychology of self, one's self-concept (also called self-construction, self-identity, self-perspective or self-structure) is a collection of beliefs
Self-concept
Psychological concepts often used in connection with narcissism
true self (also known as real self, authentic self, original self and vulnerable self) and the false self (also known as fake self, idealized self, superficial
True_self_and_false_self
1872 rhyme by Augustus De Morgan
velocity, And little whirls have lesser whirls And so on to viscosity ... Self-similarity Turtles all the way down For example: Snyed, JR (2019). "Who watches
Siphonaptera_(poem)
Fractal constructible with L-systems
iteration in reverse order with the L and R letters swapped. Many self-similarities can be seen in the Heighway dragon curve. The most obvious is the
Dragon_curve
Nonfiction book by James Gleick
the lens of four themes: sensitive dependence on initial conditions, self-similarity, universality, and nonlinearity. An enhanced ebook edition was released
Chaos:_Making_a_New_Science
Technique of placing a copy of an image within itself, or a story within a story
Self-replicating program Recursion – Process of repeating items in a self-similar way Self-similarity – Whole of an object being mathematically similar to part of
Mise_en_abyme
Human emotional need
qualities that led each to become self-actualized. In his studies, Maslow found that self-actualizers really do share similarities. He also believed that each
Self-actualization
Scientific subjects
interconnections, continuous feedback mechanisms, repetitions, self-similarity, fractals, and self-organization. The butterfly effect, a fundamental concept
Branches_of_physics
2026 single by Temper City
The song quickly gained widespread recognition, due to its stylistic similarities to 2010s indie rock bands such as Cage the Elephant and The Neighbourhood
Self_Aware
Mathematics of number-placement puzzle
these conjugacy classes represent the different types of symmetry (self-similarity or automorphism) that can be found in completed sudoku grids. Using
Mathematics_of_Sudoku
German polymath (1646–1716)
fractal geometry promoted by Mandelbrot drew on Leibniz's notions of self-similarity and the principle of continuity: Natura non facit saltus. We also see
Gottfried_Wilhelm_Leibniz
Musical artist
(2015:316), On Musical Self-Similarity "is an intriguing treatise in which repetition is generalized to several modes of self-similarity that are ubiquitous
Gabriel_Pareyon
under many guises in nature) logarithmic spiral for its property of self-similarity. Coming from this, Spira mirabilis has no fixed set-up, but it answers
Spira_mirabilis_(orchestra)
Measure of the degree to which a geometric shape is compact
volume ratio Roundness How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension "Measuring Compactness". Retrieved 22 Jan
Compactness_measure
Software bug that seems to change when debugging
term also refers to a bug that exhibits fractal behavior (that is, self-similarity) by revealing more bugs (the deeper a developer goes into the code
Heisenbug
Topics referred to by the same term
proportion and balance. The second is an exact mathematical "patterned self-similarity" that can be demonstrated with the rules of a formal system, such as
Duplication
Function with unusual fractal properties
for positive integers a1, a2, a3, …. Each such element describes a self-similarity of the question-mark function. This monoid is sometimes called the
Minkowski's question-mark function
Minkowski's_question-mark_function
Physics theory
Wainwright, J.; Hancock, M. J.; Uggla, C. (1999-08-01). "Asymptotic self-similarity breaking at late times in cosmology". Classical and Quantum Gravity
Ehlers–Geren–Sachs_theorem
American mathematician (born 2003)
1093/imrn/rnac203. ISSN 1073-7928. Larsen, Daniel (2020). "Focusing Sequences and Self-Similarity". The Fibonacci Quarterly. 58 (3): 231–240. doi:10.1080/00150517.2020
Daniel_Larsen_(mathematician)
Signal with equal energy per octave
G. (2011). On Musical Self-Similarity, International Semiotics Institute & University of Helsinki. "On Musical Self-Similarity" (PDF). "Noise in Man-generated
Pink_noise
(1999) Self-similarity in the distribution and abundance of species. Science 294, 334–336.[12] Hui, C. & McGeoch, M.A. (2007) A self-similarity model for
Scaling_pattern_of_occupancy
Geometric transformation that preserves lines but not angles nor the origin
Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, hyperbolic rotation, shear mapping, and compositions
Affine_transformation
Fractal curve
present in a great number of properties listed below. The number of self-similarities at level n is a Fibonacci number \ −1. (more precisely: F 3 n + 3
Fibonacci_word_fractal
Complex plane fractal
lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal A zoom-in to line on the left of the fractal
Burning_Ship_fractal
Software that systematically browses the World Wide Web
Mccurley, K. S.; Rajagopalan, S.; Sivakumar, D.; Tomkins, A. (2002). "Self-similarity in the web" (PDF). ACM Transactions on Internet Technology. 2 (3):
Web_crawler
Mathematical technique in data science
is termed scale invariance, and can be further categorized as self-similarity or self-affinity, the latter scaled anisotropically (depending on the direction)
Fractal_analysis
Software generating fractal images
This includes the characteristics of fractal dimension, recursion and self-similarity exhibited by all fractals. There are many fractal generating programs
Fractal-generating_software
Law in seismology describing earthquake frequency and magnitude
attempts to understand the law involve theories of self-organized criticality or self similarity. New models show a generalization of the original Gutenberg–Richter
Gutenberg–Richter_law
Topics referred to by the same term
(tour), by Keane Symmetry, a harmonious proportionality, or "patterned self-similarity" This disambiguation page lists articles associated with the title
Perfect_Symmetry
Concept in metric geometry
space, so uniqueness implies a form of metric self-similarity. The word "cone" denotes this self-similarity under dilations. Existence is not automatic
Metric_tangent_cone
Process in bioinformatics that identifies equivalent sites within molecular sequences
arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships
Sequence_alignment
Rock type formed by lightning strike
can be porous or smooth. Branching fulgurites display fractal-like self-similarity and structural scale invariance as a macroscopic or microscopic network
Fulgurite
Machine learning technique useful for dimensionality reduction
A self-organizing map (SOM) or self-organizing feature map (SOFM) is an unsupervised machine learning technique used to produce a low-dimensional (typically
Self-organizing_map
N-ary tree or a Cayley tree. Hutchinson, John E. (1981). "Fractals and self similarity". Indiana Univ. Math. J. 30 (5): 713–747. doi:10.1512/iumj.1981.30
Hutchinson_operator
Unpredictable phenomenon in complex systems
Smith, Reginald D. (2008), "The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena", Advances in Complex Systems
Emergence
Function on an integer n which is log(p) if n equals p^k and zero otherwise
applications in cryptography, physics, digital information, computing, and self-similarity. Springer Series in Information Sciences. Vol. 7 (3rd ed.). Berlin:
Von_Mangoldt_function
Visible regularity of form found in the natural world
wrote a famous paper, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, crystallising mathematical thought into the
Patterns_in_nature
Concept of art that can be described by a computer program
discovering regularities such as repetitions and symmetries and fractal self-similarity. When the observer's learning process (which may be a predictive neural
Low-complexity_art
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SELF SIMILARITY
SELF SIMILARITY
Boy/Male
Welsh
peace'.
Girl/Female
British, English
Soft
Male
Yiddish
(סֶעף) Variant spelling of Yiddish Zeff, SEFF means "wolf."
Girl/Female
Hebrew Biblical
Rock.
Biblical
a rock
Surname or Lastname
English
English : from Middle English selle, a rough hut of the type normally occupied by animals, hence a topographic name for someone who lived in a hut like this. In many cases the name may have been in effect a metonymic occupational name for a herdsman.Americanized spelling of Hungarian and Hungarian Jewish Széll, a topographic name for someone who lived in a spot exposed to the wind, from Hungarian szél ‘wind’.German : variant of Selle.
Male
Welsh
Welsh form of Greek SolomÅn, SELYF means "peaceable."Â
Surname or Lastname
English (East Anglia)
English (East Anglia) : from the Middle English personal name Saulf, Old English Sǣwulf, composed of the elements sǣ ‘sea’ + wulf ‘wolf’.
Boy/Male
Muslim
Sword
Girl/Female
African, Australian, British, Chinese, Christian, English, French, Greek, Hawaiian, Hebrew
Saviour; Ewe of West Africa; Goddess of the Moon; Cliff; Rock
Female
Egyptian
, a form of Isis.
Boy/Male
Muslim/Islamic
Sword
Boy/Male
Biblical
A rock.
Girl/Female
Egyptian
Boy/Male
Hindi
Self.
Boy/Male
Indian
Sword
Boy/Male
British, English, Nigerian, Norwegian
Rock
Boy/Male
African, Arabic, Hindu, Indian, Muslim, Sindhi, Swahili
Sword; Brave; Sword of Religion
Boy/Male
British, English, Hebrew
A Tree
Male
English
(סֶלַע) Anglicized form of Hebrew Cela, SELA means "a rock." In the Old Testament bible, this is the name of the capital city of Edom, possibly an early name for Petra. In use as a unisex name.
SELF SIMILARITY
SELF SIMILARITY
SELF SIMILARITY
SELF SIMILARITY
SELF SIMILARITY
SELF SIMILARITY
SELF SIMILARITY
n.
Self-denial; self-renunciation; self-sacrifice.
n.
Self-love.
n.
The act of governing one's self, or the state of being governed by one's self; self-control; self-command.
n.
The destruction of one's self; self-murder; suicide.
n.
Self-deceit.
a.
Self-repelling.
a.
Disposed to self-assertion; self-asserting.
n.
Restraint over one's self; self-control; self-command.
n.
Imposture practiced on one's self; self-deceit.
n.
Control of one's self; restraint exercised over one's self; self-command.
n.
The idolizing of one's self; immoderate self-conceit.
a.
Dependent on one's self; self-depending; self-reliant.
n.
The act of estimating one's self; self-esteem.
n.
Self-devotion.
n.
Faith in one's self; self-reliance.
n.
Self.
n.
Self-communion.
n.
Enjoyment of one's self; self-satisfaction.
a.
Refusing to gratify one's self; self-sacrificing.
n.
Communion with one's self; thoughts about one's self.
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