fractal dimension

collocation in English

meaningsoffractalanddimension

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withdimension.
fractal
noun[C]
uk
/ˈfræk.təl/us
/ˈfræk.təl/
a complicated pattern in mathematics built from simple repeated shapes that are reduced in size every time they ...
See more atfractal
dimension
noun
uk
/ˌdaɪˈmen.ʃən/us
/ˌdaɪˈmen.ʃən/
a measurement of something in a particular direction, especially its height, length, ...
See more atdimension

(Definition offractalanddimensionfrom theCambridge English Dictionary© Cambridge University Press)

Examplesoffractal dimension

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
The scaling for both jets and wakes extends over the entire range available; the averagefractaldimensionis 2.35k0.04 for both flows.
From theCambridge English Corpus
In this article we study two exponent measures of the structure of the tree: thefractaldimensionand the resistance dimension.
From theCambridge English Corpus
Fractaldimensioncan be quantified in terms of capacity dimension and correlation dimension.
From theCambridge English Corpus
However, there are many other transformations which preserve thefractaldimension.
From theCambridge English Corpus
Thefractaldimensionof sets derived from complex basis.
From theCambridge English Corpus
In general thefractaldimensionof a fractal antenna is a poor predictor of its performance and application.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
The uncertainty exponent is ideally tailored to measure thefractaldimensionof this type of system.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
If the theoreticalfractaldimensionof a set exceeds its topological dimension, the set is considered to have fractal geometry.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Several formal mathematical definitions of different types offractaldimensionare listed below.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
The levels are related by a ratio called thefractaldimension.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Fractaldimensionis altered in some motor dysfunctions.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
This would correspond to afractaldimensionof 2.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Thefractaldimensionis approximately 2.473946 (1 in the last digit).
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Instead, afractaldimensionmeasures complexity, a concept related to certain key features of fractals: self-similarity and detail or irregularity.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Pietronero argues that the universe shows a definite fractal aspect, over a fairly wide range of scale, with afractaldimensionof about 2.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
For example, in 2 thefractaldimensionis, for 3 it is close to while for thefractaldimensionis.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
Thefractaldimensionof a single contour will be between 1 and 2.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
The figure below shows thefractaldimensionof an advected contour as a function of time, measured in four different ways.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
There is a relationship between chaos and fractalsthe "strange attractors" in chaotic systems have afractaldimension.
From
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
Want to learn more?
Go to the definition offractal
Go to the definition ofdimension
See other collocations withdimension