Definition of fractal in English:

fractal

noun ˈfrakt(ə)lˈfræktəl

Mathematics

A curve or geometrical figure, each part of which has the same statistical character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation.
分形
Example sentencesExamples
- Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied.
- Importantly, such objects, known as fractals, turn out to be very useful for describing the shapes of physical objects such as mountains, coast lines, fractures, cracks and so on.
- Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale.
- He argued that the combination of the personal computer, the Internet, and interest in fractals, chaos, and related mathematical topics has in recent years greatly facilitated the intertwining of art and math.
- For example, we observe the presence of coexisting lipid phases (one phase less ordered than the other phase) and unstable domain growth that results in patterns such as fractals.
- Nature builds its fractals using statistical self-similarity: the patterns observed at different magnifications, although not identical, are described by the same statistics.
- Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind.
- He likes problems in diverse fields (harmonic analysis, fractals, and tilings, to name a few) that involve algebraic integers, such as Pisot and Salem numbers.
- He showed how fractals can occur in many different places in both mathematics and elsewhere in nature.
- Computer programs help diagram elaborate formations of tiny spirals that form massive, spiraled fractals to describe, say, the economic tendencies of your new, island society.
- Related, but not directly, I have spent much time getting to know fractals, 4d geometry, and other ‘strange’ mathematical phenomena.
- Mathematicians can use similar algorithms to generate fractals and other forms.
- But as the technology and computing power advanced, those working on the project would test more and more complex patterns, such as the most obvious candidates - fractals.
- The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals.
- The implications of map theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science.
- Many natural chaotic systems form fractals in the patterns that record the process.
- Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings.
- The researchers discovered that Pollock's patterns could be characterized as fractals - shapes that repeat themselves on different scales within the same object.
- The new sciences of complexity - fractals, nonlinear dynamics, the new cosmology, self-organizing systems - have brought about the change in perspective.
- Mathematicians have long been taken with the concept of fractals, which posits that patterns are made up of smaller, self-contained patterns.

adjective ˈfrakt(ə)lˈfræktəl

Mathematics

Relating to or of the nature of a fractal or fractals.
（与）分形（有关）的
fractal geometry
分形几何。
Example sentencesExamples
- While classical geometry assumes that objects exist in integer dimensions, fractal geometry deals with objects that have non-integer dimensions.
- Each level of expression contributed to the next, and over the course of millennia we created mathematical theory, from basic arithmetic to algebra, from calculus to fractal geometry.
- Chaos theory is everywhere now: landscapes and starscapes in sci-fi movies, image compression software, even your laser printer uses fractal algorithms.
- His unique knowledge of subjects such as fractal dynamics, subspace theory, a tri-vector system and others, has made this energetic feedback system possible.
- His research focuses on the interplay between fractal geometry and stochastic processes.
- During this time the writer also became increasingly curious about the link between science and spiritual potential, developing a keen interest in fractal geometry, quantum mechanics and chaos theory.
- A number of fractal dimension algorithms were developed and evaluated using a field data set of 100 incidents.
- Then we study the technique formally, and then apply it to images of fractal art.
- Would the present obsession with fractal geometry have come about anyway as part of the ever changing taste of architectural stylists, or is it an inevitable result of computer power?
- To explain the concept of fractal dimension, it is necessary to understand what we mean by dimension in the first place.
- It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity.
- The current visual novelty of abstractions derived from digital technology, fractal geometry and literary theory is usually the product of inventive imagination rather than empathic imagination.
- The first condition that must be fulfilled to apply scaling analysis techniques is that the growth behavior of a process lie in the fractal nature of the interface.
- More precisely, the recursive nature, which is essential for fractal models, is lacking in the procedural approach.
- This result also solved a long-standing open problem concerning the existence of certain fractal sets in the plane.
Synonyms
unmethodical, uncoordinated, undirected, disorganized, unarranged, unplanned, unpremeditated, indiscriminate

Origin

1970s: from French, from Latin fract- 'broken', from the verb frangere.

Definition of fractal in US English:

fractal

nounˈfraktəlˈfræktəl

Mathematics

A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.
分形
Example sentencesExamples
- But as the technology and computing power advanced, those working on the project would test more and more complex patterns, such as the most obvious candidates - fractals.
- Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind.
- Many natural chaotic systems form fractals in the patterns that record the process.
- Related, but not directly, I have spent much time getting to know fractals, 4d geometry, and other ‘strange’ mathematical phenomena.
- Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied.
- Mathematicians can use similar algorithms to generate fractals and other forms.
- Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale.
- The implications of map theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science.
- For example, we observe the presence of coexisting lipid phases (one phase less ordered than the other phase) and unstable domain growth that results in patterns such as fractals.
- Mathematicians have long been taken with the concept of fractals, which posits that patterns are made up of smaller, self-contained patterns.
- He showed how fractals can occur in many different places in both mathematics and elsewhere in nature.
- He likes problems in diverse fields (harmonic analysis, fractals, and tilings, to name a few) that involve algebraic integers, such as Pisot and Salem numbers.
- The new sciences of complexity - fractals, nonlinear dynamics, the new cosmology, self-organizing systems - have brought about the change in perspective.
- Importantly, such objects, known as fractals, turn out to be very useful for describing the shapes of physical objects such as mountains, coast lines, fractures, cracks and so on.
- Computer programs help diagram elaborate formations of tiny spirals that form massive, spiraled fractals to describe, say, the economic tendencies of your new, island society.
- He argued that the combination of the personal computer, the Internet, and interest in fractals, chaos, and related mathematical topics has in recent years greatly facilitated the intertwining of art and math.
- The researchers discovered that Pollock's patterns could be characterized as fractals - shapes that repeat themselves on different scales within the same object.
- Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings.
- The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals.
- Nature builds its fractals using statistical self-similarity: the patterns observed at different magnifications, although not identical, are described by the same statistics.

adjectiveˈfraktəlˈfræktəl

Mathematics

Relating to or of the nature of a fractal or fractals.
（与）分形（有关）的
fractal geometry
分形几何。
Example sentencesExamples
- While classical geometry assumes that objects exist in integer dimensions, fractal geometry deals with objects that have non-integer dimensions.
- Would the present obsession with fractal geometry have come about anyway as part of the ever changing taste of architectural stylists, or is it an inevitable result of computer power?
- The first condition that must be fulfilled to apply scaling analysis techniques is that the growth behavior of a process lie in the fractal nature of the interface.
- His unique knowledge of subjects such as fractal dynamics, subspace theory, a tri-vector system and others, has made this energetic feedback system possible.
- This result also solved a long-standing open problem concerning the existence of certain fractal sets in the plane.
- A number of fractal dimension algorithms were developed and evaluated using a field data set of 100 incidents.
- His research focuses on the interplay between fractal geometry and stochastic processes.
- During this time the writer also became increasingly curious about the link between science and spiritual potential, developing a keen interest in fractal geometry, quantum mechanics and chaos theory.
- More precisely, the recursive nature, which is essential for fractal models, is lacking in the procedural approach.
- Each level of expression contributed to the next, and over the course of millennia we created mathematical theory, from basic arithmetic to algebra, from calculus to fractal geometry.
- Chaos theory is everywhere now: landscapes and starscapes in sci-fi movies, image compression software, even your laser printer uses fractal algorithms.
- To explain the concept of fractal dimension, it is necessary to understand what we mean by dimension in the first place.
- The current visual novelty of abstractions derived from digital technology, fractal geometry and literary theory is usually the product of inventive imagination rather than empathic imagination.
- Then we study the technique formally, and then apply it to images of fractal art.
- It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity.
Synonyms
unmethodical, uncoordinated, undirected, disorganized, unarranged, unplanned, unpremeditated, indiscriminate

Origin

1970s: from French, from Latin fract- ‘broken’, from the verb frangere.

词汇	fractal
释义	Definition of fractal in English: fractal noun ˈfrakt(ə)lˈfræktəl Mathematics A curve or geometrical figure, each part of which has the same statistical character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation. 分形 Example sentencesExamples Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied. Importantly, such objects, known as fractals, turn out to be very useful for describing the shapes of physical objects such as mountains, coast lines, fractures, cracks and so on. Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale. He argued that the combination of the personal computer, the Internet, and interest in fractals, chaos, and related mathematical topics has in recent years greatly facilitated the intertwining of art and math. For example, we observe the presence of coexisting lipid phases (one phase less ordered than the other phase) and unstable domain growth that results in patterns such as fractals. Nature builds its fractals using statistical self-similarity: the patterns observed at different magnifications, although not identical, are described by the same statistics. Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind. He likes problems in diverse fields (harmonic analysis, fractals, and tilings, to name a few) that involve algebraic integers, such as Pisot and Salem numbers. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. Computer programs help diagram elaborate formations of tiny spirals that form massive, spiraled fractals to describe, say, the economic tendencies of your new, island society. Related, but not directly, I have spent much time getting to know fractals, 4d geometry, and other ‘strange’ mathematical phenomena. Mathematicians can use similar algorithms to generate fractals and other forms. But as the technology and computing power advanced, those working on the project would test more and more complex patterns, such as the most obvious candidates - fractals. The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals. The implications of map theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science. Many natural chaotic systems form fractals in the patterns that record the process. Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings. The researchers discovered that Pollock's patterns could be characterized as fractals - shapes that repeat themselves on different scales within the same object. The new sciences of complexity - fractals, nonlinear dynamics, the new cosmology, self-organizing systems - have brought about the change in perspective. Mathematicians have long been taken with the concept of fractals, which posits that patterns are made up of smaller, self-contained patterns. adjective ˈfrakt(ə)lˈfræktəl Mathematics Relating to or of the nature of a fractal or fractals. （与）分形（有关）的 fractal geometry 分形几何。 Example sentencesExamples While classical geometry assumes that objects exist in integer dimensions, fractal geometry deals with objects that have non-integer dimensions. Each level of expression contributed to the next, and over the course of millennia we created mathematical theory, from basic arithmetic to algebra, from calculus to fractal geometry. Chaos theory is everywhere now: landscapes and starscapes in sci-fi movies, image compression software, even your laser printer uses fractal algorithms. His unique knowledge of subjects such as fractal dynamics, subspace theory, a tri-vector system and others, has made this energetic feedback system possible. His research focuses on the interplay between fractal geometry and stochastic processes. During this time the writer also became increasingly curious about the link between science and spiritual potential, developing a keen interest in fractal geometry, quantum mechanics and chaos theory. A number of fractal dimension algorithms were developed and evaluated using a field data set of 100 incidents. Then we study the technique formally, and then apply it to images of fractal art. Would the present obsession with fractal geometry have come about anyway as part of the ever changing taste of architectural stylists, or is it an inevitable result of computer power? To explain the concept of fractal dimension, it is necessary to understand what we mean by dimension in the first place. It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity. The current visual novelty of abstractions derived from digital technology, fractal geometry and literary theory is usually the product of inventive imagination rather than empathic imagination. The first condition that must be fulfilled to apply scaling analysis techniques is that the growth behavior of a process lie in the fractal nature of the interface. More precisely, the recursive nature, which is essential for fractal models, is lacking in the procedural approach. This result also solved a long-standing open problem concerning the existence of certain fractal sets in the plane. Synonyms unmethodical, uncoordinated, undirected, disorganized, unarranged, unplanned, unpremeditated, indiscriminate Origin 1970s: from French, from Latin fract- 'broken', from the verb frangere. Definition of fractal in US English: fractal nounˈfraktəlˈfræktəl Mathematics A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. 分形 Example sentencesExamples But as the technology and computing power advanced, those working on the project would test more and more complex patterns, such as the most obvious candidates - fractals. Some of the complexity has been captured in modern pictures of fractals, many of which are created by iterating functions of this kind. Many natural chaotic systems form fractals in the patterns that record the process. Related, but not directly, I have spent much time getting to know fractals, 4d geometry, and other ‘strange’ mathematical phenomena. Strange attractors have detailed structure on all scales of magnification and were one of the early fractals to be studied. Mathematicians can use similar algorithms to generate fractals and other forms. Like a mountain range whose profile appears equally craggy when observed from both far and near, fractals are used to define curves and surfaces, independent of their scale. The implications of map theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science. For example, we observe the presence of coexisting lipid phases (one phase less ordered than the other phase) and unstable domain growth that results in patterns such as fractals. Mathematicians have long been taken with the concept of fractals, which posits that patterns are made up of smaller, self-contained patterns. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. He likes problems in diverse fields (harmonic analysis, fractals, and tilings, to name a few) that involve algebraic integers, such as Pisot and Salem numbers. The new sciences of complexity - fractals, nonlinear dynamics, the new cosmology, self-organizing systems - have brought about the change in perspective. Importantly, such objects, known as fractals, turn out to be very useful for describing the shapes of physical objects such as mountains, coast lines, fractures, cracks and so on. Computer programs help diagram elaborate formations of tiny spirals that form massive, spiraled fractals to describe, say, the economic tendencies of your new, island society. He argued that the combination of the personal computer, the Internet, and interest in fractals, chaos, and related mathematical topics has in recent years greatly facilitated the intertwining of art and math. The researchers discovered that Pollock's patterns could be characterized as fractals - shapes that repeat themselves on different scales within the same object. Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings. The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals. Nature builds its fractals using statistical self-similarity: the patterns observed at different magnifications, although not identical, are described by the same statistics. adjectiveˈfraktəlˈfræktəl Mathematics Relating to or of the nature of a fractal or fractals. （与）分形（有关）的 fractal geometry 分形几何。 Example sentencesExamples While classical geometry assumes that objects exist in integer dimensions, fractal geometry deals with objects that have non-integer dimensions. Would the present obsession with fractal geometry have come about anyway as part of the ever changing taste of architectural stylists, or is it an inevitable result of computer power? The first condition that must be fulfilled to apply scaling analysis techniques is that the growth behavior of a process lie in the fractal nature of the interface. His unique knowledge of subjects such as fractal dynamics, subspace theory, a tri-vector system and others, has made this energetic feedback system possible. This result also solved a long-standing open problem concerning the existence of certain fractal sets in the plane. A number of fractal dimension algorithms were developed and evaluated using a field data set of 100 incidents. His research focuses on the interplay between fractal geometry and stochastic processes. During this time the writer also became increasingly curious about the link between science and spiritual potential, developing a keen interest in fractal geometry, quantum mechanics and chaos theory. More precisely, the recursive nature, which is essential for fractal models, is lacking in the procedural approach. Each level of expression contributed to the next, and over the course of millennia we created mathematical theory, from basic arithmetic to algebra, from calculus to fractal geometry. Chaos theory is everywhere now: landscapes and starscapes in sci-fi movies, image compression software, even your laser printer uses fractal algorithms. To explain the concept of fractal dimension, it is necessary to understand what we mean by dimension in the first place. The current visual novelty of abstractions derived from digital technology, fractal geometry and literary theory is usually the product of inventive imagination rather than empathic imagination. Then we study the technique formally, and then apply it to images of fractal art. It should be remembered that in his era there was little thought or knowledge of fractal geometry, curved space or different degrees of infinity. Synonyms unmethodical, uncoordinated, undirected, disorganized, unarranged, unplanned, unpremeditated, indiscriminate Origin 1970s: from French, from Latin fract- ‘broken’, from the verb frangere.
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