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Image compression technique
The fractal transform is a technique invented by Michael Barnsley et al. to perform lossy image compression. It is a fractal compression system for digital
Fractal_transform
Compression method for digital images
Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying
Fractal_compression
(data compression) Chirplet transform Distance transform Fractal transform Gelfand transform Hadamard transform Hough transform (digital image processing)
List_of_transforms
Fractal which resembles a plant
The Barnsley fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book Fractals Everywhere. He made it
Barnsley_fern
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
Dragon curve Fatou set Fractal Fractal antenna Fractal art Fractal compression Fractal flame Fractal landscape Fractal transform Fractint Graftal Iterated
Index of fractal-related articles
Index_of_fractal-related_articles
Method for the construction of fractals
method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were
Iterated_function_system
Fractal functions in mathematics
Fractal flames are a member of the iterated function system class of fractals created by Scott Draves in 1992. Draves' open-source code was later ported
Fractal_flame
Algorithm used in data compression
The Burrows–Wheeler transform (BWT) rearranges a character string into runs of similar characters, in a manner that can be reversed to recover the original
Burrows–Wheeler_transform
American ethnobotanist, lecturer, and writer (1946–2000)
civilization. McKenna formulated a concept about the nature of time based on fractal patterns he claimed to have discovered in the I Ching, which he called
Terence_McKenna
System with multiple fractal dimensions
A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics;
Multifractal_system
Open problem on 3x+1 and x/2 functions
Julia set of f {\displaystyle f} , which forms a fractal pattern, sometimes called a "Collatz fractal". There are many other ways to define a complex interpolating
Collatz_conjecture
Method for detecting a signal's fractal dimension
The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal. More than this, the WTMM is capable of partitioning
Wavelet transform modulus maxima method
Wavelet_transform_modulus_maxima_method
Field of mathematics and science based on non-linear systems and initial conditions
interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization. The butterfly effect, an underlying principle of
Chaos_theory
Open subset of the real–number line
An ordinary fractal string Ω {\displaystyle \Omega } is a bounded, open subset of the real number line. Such a subset can be written as an at-most-countable
Fractal_string
Open Source fractal editor and generator
open source fractal flame editor and renderer for Microsoft Windows and Macintosh. Apophysis has many features for creating and editing fractal flames, including
Apophysis_(software)
Iranian artist
real-life objects, intricate and symmetrical illustrations, animations, fractals and tessellations. Naderi Yeganeh uses mathematics as the main tool to
Hamid_Naderi_Yeganeh
Rational function of the form (az + b)/(cz + d)
Möbius group is the modular group; it is central to the theory of many fractals, modular forms, elliptic curves and Pellian equations. Möbius transformations
Möbius_transformation
Digital painting software
light and dark interface theme. The Pro edition featured Fractal Image Processing for Transform, Liquify and Canvas Size tools for keeping the best quality
Rebelle_(software)
Geometric transformation that preserves lines but not angles nor the origin
Operations: Affine Transform, R. Fisher, S. Perkins, A. Walker and E. Wolfart. Weisstein, Eric W. "Affine Transformation". MathWorld. Affine Transform by Bernard
Affine_transformation
Three-dimensional fractal
The Mandelbulb is a three-dimensional fractal developed in 2009 by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional
Mandelbulb
Signal with equal energy per octave
this file? See media help. Pink noise, 1/f noise, fractional noise or fractal noise is a signal or process with a frequency spectrum such that the power
Pink_noise
Generalization of derivative to fractals
time are to be transformed according to (xβ, tα). Elementary physical concepts such as velocity are redefined as follows for fractal spacetime (xβ, tα):
Fractal_derivative
Raster-based digital painting software
for the Macintosh system by Mark Zimmer and Tom Hedges, founders of the Fractal Design Corporation. Zimmer and Hedges had previously developed ImageStudio
Corel_Painter
Compact encoding of digital data
cosine transform Discrete sine transform Discrete wavelet transform Embedded zerotrees of wavelet transforms Fractal compression Lapped transform Line spectral
Data_compression
Whole of an object being mathematically similar to part of itself
contains an exact replica of the whole figure. Since mathematically, a fractal may show self-similarity under arbitrary magnification, it is impossible
Self-similarity
Mathematical function, inverse of an exponential function
measurements of the complexity of algorithms and of geometric objects called fractals. They help to describe frequency ratios of musical intervals, appear in
Logarithm
Fractal-generating computer program
Sterling is a fractal-generating computer program written in the C programming language in 1999 for Microsoft Windows by Stephen C. Ferguson. Sterling
Sterling_(program)
Integral transform generalizing both Laplace and Sumudu transforms
mathematics, the Shehu transform is an integral transform which generalizes both the Laplace transform and the Sumudu integral transform. It was introduced
Shehu_transform
Geometrical property
transforms is also a transform and every transform has, by definition, an inverse transform that undoes it, the set of transforms under which an object
Symmetry_(geometry)
Rewriting system and type of formal grammar
morphology of a variety of organisms and can be used to generate self-similar fractals. As a biologist, Lindenmayer worked with yeast and filamentous fungi and
L-system
Image edge detection algorithm
Poznan, Poland, September 3–7, 2007. Wikibooks has a book on the topic of: Fractals/Computer_graphic_techniques/2D#Sobel_filter Sobel edge detection in OpenCV
Sobel_operator
Type of data compression
Fractal compression JBIG2 (lossless or lossy compression) S3TC texture compression for 3D computer graphics hardware glTF Discrete cosine transform (DCT)
Lossy_compression
Two-dimensional fractal
In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing
T-square_(fractal)
Gaussian-windowed wavelet
frequency resolution. These are used in the Gabor transform, a type of short-time Fourier transform. In 1984, Jean Morlet introduced Gabor's work to the
Morlet_wavelet
Fractal curve resembling a blancmange pudding
In mathematics, the blancmange curve is a self-affine fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, after
Blancmange_curve
2002 Japanese television series
before being defeated by Mercurymon who stole is fractal code. After Mercurymon was defeated, the fractal code he stole from Seraphimon went to his egg and
Digimon_Frontier
ThePrint. Retrieved 2023-05-13. Khosla, Varuni (2022-12-09). "Indian company Fractal Picture behind Fifa World Cup Qatar 2022 mascot La'eeb". mint. Archived
List of FIFA World Cup official mascots
List_of_FIFA_World_Cup_official_mascots
Generalized function whose value is zero everywhere except at zero
the Physical and Engineering Sciences: Distributional and fractal calculus, integral transforms, and wavelets, Birkhäuser, ISBN 978-0-8176-3924-2 Schwartz
Dirac_delta_function
Function for integral Fourier-like transform
Chirplet transform Hermite polynomials Hermitian wavelet Curvelet Digital cinema Dimension reduction Filter banks Fourier-related transforms Fractal compression
Wavelet
Measure of the long-range dependence of a time series
the standard notation H for the coefficient also relates to his name. In fractal geometry, the generalized Hurst exponent has been denoted by H or Hq in
Hurst_exponent
Term in geometry and fractal analysis
specialized term in geometry referring to a measure of how patterns, especially fractals, fill space, where patterns having more or larger gaps generally have higher
Lacunarity
Fractal with a boxlike shape
In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set
Mandelbox
Fractal composed of tangent circles
an Apollonian gasket, Apollonian net, or Apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent to the other
Apollonian_gasket
Chinese five elements
Fresh Translator of Zang Xiang Fractal five System，Chinese Journal of Integrative Medicine; 1999 Deng Yu et al，TCM Fractal Sets 中医分形集, Journal of Mathematical
Wuxing_(Chinese_philosophy)
Orthogonal wavelets
broad range of problems, e.g. self-similarity properties of a signal or fractal problems, signal discontinuities, etc. The Daubechies wavelets are not
Daubechies_wavelet
Least variables needed to represent data
dimension measured is some version of fractal dimension — which also can be non-integer. However, definitions of fractal dimension yield the manifold dimension
Intrinsic_dimension
1985 video game
took advantage of the fractal technology developed for Rescue on Fractalus!, further enhancing it. In The Eidolon, Rescue's fractal mountains were turned
The_Eidolon
sequence of the first season, the Hulk picks up an Infinity Fractal, and is transformed by its power into something different every episode. This feature
List of The Super Hero Squad Show episodes
List_of_The_Super_Hero_Squad_Show_episodes
Generalization in fractional calculus
Derivative and Numerical Solutions of Fractional Differential Equations". Fractal and Fractional. 7 (10): 750. doi:10.3390/fractalfract7100750. Sikora, Beata
Caputo_fractional_derivative
Type of mathematical generalization
the study of fractals and multi-fractal measures, and expressions for the entropy of chaotic dynamical systems. The relationship to fractals and dynamical
Q-analog
finding that traditional batiks from different regions of Java have distinct fractal dimensions, and stimuli to mathematics research, especially Filippo Brunelleschi's
Mathematics_and_art
Function with unusual fractal properties
Minkowski's question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational
Minkowski's question-mark function
Minkowski's_question-mark_function
American cultural anthropologist
innovations in symbolic anthropology, kinship analysis, and his concepts of fractal personhood and holographic worldview. In 2011, Justin Shaffner accompanied
Roy_Wagner
Self-similar fractal curve
In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto
Lévy_C_curve
Reduction of image size to save storage and transmission costs
averaging or dropping some of the chrominance information in the image. Fractal compression. More recently, methods based on Machine Learning were applied
Image_compression
Triangular array of the binomial coefficients
coloring only the odd numbers in Pascal's triangle closely resembles the fractal known as the Sierpiński triangle. This resemblance becomes increasingly
Pascal's_triangle
Device or program that encodes/decodes audio data in some bitstream format
modern audio compression algorithms are based on modified discrete cosine transform (MDCT) coding and linear predictive coding (LPC). In hardware, audio codec
Audio_codec
Quartet of novels by Piers Anthony
force of female magic, to her home planet of Oria, which is part of a fractal universe. In order to summon the Megaplayers, a group of musical giants
Mode_(novel_series)
Differential operator in mathematics
[1994] Weisstein, Eric W. "Laplacian". MathWorld. Laplacian in polar coordinates derivation Laplace equations on the fractal cubes and Casimir effect
Laplace_operator
Simple polynomial map exhibiting chaotic behavior
topic of: Fractals/Iterations_of_real_numbers/r_iterations#Logistic_map The Chaos Hypertextbook. An introductory primer on chaos and fractals. An interactive
Logistic_map
Random walk with heavy-tailed step lengths
\\u^{-D}&:\ u\geq 1.\end{cases}}} Here D is a parameter related to the fractal dimension and the distribution is a particular case of the Pareto distribution
Lévy_flight
2010 novel by Hannu Rajeniemi
trilogy featuring the character of Jean le Flambeur; the sequels are The Fractal Prince (2012) and The Causal Angel (2014). The novel was published in Britain
The_Quantum_Thief
Tschirnhausen cubic Witch of Agnesi Ampersand curve Bean curve Bicorn Transformed bicorn Bicuspid curve Bow curve Bullet-nose curve Cruciform curve Deltoid
Gallery_of_curves
Nature-inspired design
designs are composite fractal patterns consisting of individual fractal 'tree-seeds' which combine to create a 'global fractal forest.' The local 'tree-seed'
Biophilic_design
1950 painting by Jackson Pollock
undergone fractal analysis that is being used to prove the authenticity of other Pollock works as well as to contribute more insight into fractal geometry
One:_Number_31,_1950
Continuous fractal curve obtained as the image of Cantor space
In mathematics, a de Rham curve is a continuous fractal curve obtained as the image of the Cantor space, or, equivalently, from the base-two expansion
De_Rham_curve
Metric used to measure signal quality
60 dB for images with 12 bits per color. Welstead, Stephen T. (1999). Fractal and wavelet image compression techniques. SPIE Publication. pp. 155–156
Peak_signal-to-noise_ratio
Topics referred to by the same term
from August 2007 to February 2008 Wavelet transform modulus maxima method, a method for detecting fractal dimension of a signal or time-series This disambiguation
WTMM
Fourier transform of Eq. 6 results in Eq. 1. Power-law scattering is restricted to sizes smaller than the object. For example, within a mass-fractal object
Unified_scattering_function
2023 science fiction novel by Emma Mieko Candon
a relic as Iterate Fractal dies. He finds that after his resurrection, he is unable to age or be killed. After Iterate Fractal's death, the Harbor is
The_Archive_Undying
Number, approximately 3.14
ellipses and spheres. It is found as well in formulae from cosmology, fractals, thermodynamics, mechanics, and electromagnetism. It also appears in areas
Pi
Operator in fractional calculus
West, Bruce J.; Bologna, Mauro; Grigolini, Paolo (2003). Physics of Fractal Operators. Springer Verlag. ISBN 0-387-95554-2. MathWorld – Fractional
Differintegral
Wavelet whose associated wavelet transform is orthogonal
wavelets. The scaling function is a refinable function. That is, it is a fractal functional equation, called the refinement equation (twin-scale relation
Orthogonal_wavelet
Shape with three sides
space. For example, a CAT(k) space is characterized by such comparisons. Fractal shapes based on triangles include the Sierpiński gasket and the Koch snowflake
Triangle
Technique of using algorithms to create music
composers as creative inspiration for their music. Algorithms such as fractals, L-systems, statistical models, and even arbitrary data (e.g. census figures
Algorithmic_composition
American mathematician (1943–2021)
known for his analysis on fractals, building upon the work of Jun Kigami on the construction of a Laplacian operator on fractals such as the Sierpinski–Menger
Robert_Strichartz
Dutch publishing and analytics company
"Publisher's note". Chaos, Solitons & Fractals. 39: v–. 2009. doi:10.1016/S0960-0779(09)00060-5. Chaos, Solitons and Fractals. November 2011. Archived from the
Elsevier
Continent
Africa. A common theme in traditional African architecture is the use of fractal scaling: small parts of the structure tend to look similar to larger parts
Africa
Comics character
group whose medallion is an Infinity Fractal that was sent back in time and renders him immune to other Fractals' powers. Throughout the first season
Reptil
Medical diagnostic method
Ahsan H. (2017-09-08). "Fetal Heart Sounds Detection Using Wavelet Transform and Fractal Dimension". Frontiers in Bioengineering and Biotechnology. 5 49
Phonocardiogram
Wavelet (EZW) Fast Cosine Transform algorithms (FCT algorithms): computes Discrete Cosine Transform (DCT) efficiently Fractal compression: method used
List_of_algorithms
Description of constant-temperature solid phase changes
The Avrami equation describes how solids transform from one phase to another at constant temperature. It can specifically describe the kinetics of crystallisation
Avrami_equation
Symmetrical calligraphic or typographic visual pun
shrinks in a self-similar manner, forming a fractal. In general, only a few letters are constrained in a fractal ambigram. The other letters don't need to
Ambigram
Japanese anime director and manga artist (1963–2010)
creates to his influence. Kon's idea of fractal control of film comes from Susumu Hirasawa, who has applied fractal-generating programs to music production
Satoshi_Kon
File format for block-based Gzip compression
Standard test image Texture compression Methods Chain code DCT Deflate Fractal KLT LP RLE Wavelet Daubechies DWT EZW SPIHT Video Concepts Bit rate ABR
BGZF
Random walk with random time between jumps
1007/BF01016796. Hilfer, R.; Anton, L. (1995). "Fractional master equations and fractal time random walks". Phys. Rev. E. 51 (2): R848–R851. Bibcode:1995PhRvE
Continuous-time_random_walk
Features that do not change if length or energy scales are multiplied by a common factor
sometimes said that fractals are scale-invariant, although more precisely, one should say that they are self-similar. A fractal is equal to itself typically
Scale_invariance
2002 short film by Takahiro Imamura
witnessing Darcmon transform into Hippogriffomon. Exposed while forced to become Darcmon again, the fraud reveals to have been collecting the Fractal Code to revive
Digimon Frontier: Island of Lost Digimon
Digimon_Frontier:_Island_of_Lost_Digimon
Branch of mathematical analysis
08070. doi:10.3390/math6010006. Khalili Golmankhaneh, Alireza (2022). Fractal Calculus and its Applications. Singapore: World Scientific Pub Co Inc.
Fractional_calculus
characterized by power-law nonlocality, power-law long-range dependence or fractal properties. Fractional-order systems are useful in studying the anomalous
Fractional-order_system
Mathematical function common in physics
exponential is also the characteristic function, basically the Fourier transform, of the Lévy symmetric alpha-stable distribution. In physics, the stretched
Stretched exponential function
Stretched_exponential_function
chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow. The flow is characterized by an exponential
Chaotic_mixing
Computer art form using text characters
calculated images, such as mandelbrot fractal animations. There are now many tools and programs that can transform raster images into text symbols; some
ASCII_art
Multimedia framework
Intel Music Coder, and Indeo Audio Coder RealNetworks Video RealVideo Fractal Codec (a.k.a. Iterated Systems ClearVideo), 1, 2, 3 and 4 Audio RealAudio
FFmpeg
British theoretical physicist and mathematician (1923–2020)
Dyson originated several concepts that bear his name, such as Dyson's transform, a fundamental technique in additive number theory, which he developed
Freeman_Dyson
British and American writer and lecturer (1915–1973)
features original voice recordings of Watts’s teachings set to synchronized fractal animations and a surround-sound score. The production has been exhibited
Alan_Watts
Art created digitally with a computer
about the art form". Digital art can be purely computer-generated (such as fractals and algorithmic art) or taken from other sources, such as a scanned photograph
Digital_art
Science fiction series by David Brin
root stock of the Tytlal race, and actual Tytlals passing as beasts. The Fractal World is an enormous, hollow artificial structure built around a dying
Uplift_Storm_trilogy
Method to detect power-law scaling in time series
Therefore, the DFA scaling exponent α {\displaystyle \alpha } is not a fractal dimension, and does not have certain desirable properties that the Hausdorff
Detrended fluctuation analysis
Detrended_fluctuation_analysis
FRACTAL TRANSFORM
FRACTAL TRANSFORM
Surname or Lastname
English
English : habitational name from Pontefract in Yorkshire, formerly pronounced and sometimes spelled ‘Pomfret’. The place name is from Latin pons, pontis ‘bridge’ + fractus ‘broken’.
Girl/Female
Greek
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Biblical
to whisper; an embalmer; a village of the tribe of David
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Boy/Male
Hindu, Indian
Peacock
Surname or Lastname
English and French
English and French : regional name from Old French Poitevin, denoting someone from Poitou in western France. The form Potvin has long been established in England and was brought to the U.S. from there. However, French bearers of the surname Poitevin also came to the New World, where their surname underwent a similar transformation on arrival in New England.
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Surname or Lastname
English
English : habitational name from Lichfield in Staffordshire. The first element preserves a British name recorded as Letocetum during the Romano-British period. This means ‘gray wood’, from words which are the ancestors of Welsh llŵyd ‘gray’ and coed ‘wood’. By the Old English period this had been reduced to Licced, and the element feld ‘pasture’, ‘open country’ was added to describe a patch of cleared land within the ancient wood.English : habitational name from Litchfield in Hampshire, recorded in Domesday Book as Liveselle. This is probably from an Old English hlīf ‘shelter’ + Old English scylf ‘shelf’, ‘ledge’. The subsequent transformation of the place name may be the result of folk etymological association with Old English hlið, hlid ‘slope’ + feld ‘open country’.
Girl/Female
Israeli
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Most beautiful. In Mythology the Arcadian nymph Calista transformed into a she-bear; then into...
Boy/Male
Biblical
To whisper; an embalmer.
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Boy/Male
Czechoslovakian Teutonic Czech
Free.
FRACTAL TRANSFORM
FRACTAL TRANSFORM
Female
Hebrew
Variant spelling of Hebrew Danya, DANIAH means "judge."
Girl/Female
Christian & English(British/American/Australian)
Crimson or Red
Girl/Female
Italian Latin
From the Tiber.
Surname or Lastname
English and French
English and French : variant of Gault.
Boy/Male
Armenian, Australian, French, German
Guardian; Mighty with a Spear
Female
Egyptian
, a daughter of Amenhotep IV.
Girl/Female
Tamil
Bird, Hot
Boy/Male
Hindu, Indian
Duty
Girl/Female
Muslim
Most beautiful (Hoor in Jannah)
Girl/Female
Greek, Gujarati, Indian, Kannada, Russian, Swedish, Traditional
Light; Torch; Moon; Glow
FRACTAL TRANSFORM
FRACTAL TRANSFORM
FRACTAL TRANSFORM
FRACTAL TRANSFORM
FRACTAL TRANSFORM
n.
The metal face guard of a soldier.
a.
Belonging to the front part; being in front
a.
Situated behind the frontal bone or the frontal region of the skull; -- applied especially to a bone back of and below the frontal in many animals.
a.
Having the nature or appearance of a bract.
a.
Of or pertaining to the forehead or the anterior part of the roof of the brain case; as, the frontal bones.
n.
An ornamental band for the hair.
a.
Relating to, or containing, facts.
a.
Destructive; fatal.
n.
The frontal bone, or one of the two frontal bones, of the cranium.
n.
A little pediment over a door or window.
a.
Of or pertaining to a race or family of men; as, the racial complexion.
n.
A movable, decorative member in metal, carved wood, or, commonly, in rich stuff or in embroidery, covering the front of the altar. Frontals are usually changed according to the different ceremonies.
n.
A medicament or application for the forehead.
a.
Causing death or destruction; deadly; mortal; destructive; calamitous; as, a fatal wound; a fatal disease; a fatal day; a fatal error.
n.
Same as Frontal, 2.
n.
Something worn on the forehead or face; a frontlet
n.
Facial neuralgia.
a.
Of or pertaining to the forehead or frontal bones; frontal; as, the metopic suture.
a.
Of or pertaining to the face; as, the facial artery, vein, or nerve.
a.
Of or pertaining to the rictus; as, rictal bristles.