What is meant by self-similarity?
An object is said to be self-similar if it looks “roughly” the same on any scale. Fractals are a particularly interesting class of self-similar objects.
Are hexagons self-similar?
Neither the rhombus nor the hexagon is a self-similar fractal, but a clever subdivision of these elements will, nevertheless, allow us to determine their stiffness by means of the similarity principle.
What does it mean by self-similarity in mathematics?
fractals
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Self-similarity is a typical property of fractals.
What is an example of self-similarity?
The property of having a substructure analogous or identical to an overall structure. For example, a part of a line segment is itself a line segment, and thus a line segment exhibits self-similarity. By contrast, no part of a circle is a circle, and thus a circle does not exhibit self-similarity.
How do you determine self-similarity?
Similarly, a two dimensional object, such as a square, can be divided into N self-similar parts, each part being scaled down by the factor r = 1/N(1/2) (i.e. if you cut a square into 4 equally-sized squares, then each new square is half the size (side length) of the original square).
What is difference between self-similar and strictly self-similar?
If parts of a figure contain small replicas of the whole, then the figure is called self-similar. If the figure can be decomposed into parts which are exact replicas of the whole, then the figure is called strictly self-similar.
What is another term for self-similarity?
In this page you can discover 12 synonyms, antonyms, idiomatic expressions, and related words for self-similar, like: birth-death, Ornstein-Uhlenbeck, , self-affine, topological, higher-dimensional, self-similarity, fractal, hyperbolic, low-dimensional and quasiperiodic.
Which of the following are examples of self-similarity occurring in nature?
Fractals in nature These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, mountains, river networks, cauliflower or broccoli, and systems of blood vessels.
What polygons are self-similar?
Except for non-isosceles right triangles, the golden bee is the only polygon that can be partitioned into a non-congruent pair of scaled copies of itself [16]. Figure 3. The golden bee is an example of a self-similar polygon.
Is the Sierpinski triangle strictly self-similar?
The Sierpinski Triangle A striking feature of the Sierpinski triangle is its strict self- similarity. Since each and every part of the Sierpinski triangle has this property, it is also strictly self-similar.
What is a fractal self-similar?
Simply put, a fractal is a geometric object that is similar to itself on all scales. If you zoom in on a fractal object it will look similar or exactly like the original shape. This property is called self-similarity. The property of self-similarity or scaling is closely related to the notion of dimension. …
Which is the best definition of self similarity?
Freebase (0.00 / 0 votes)Rate this definition: Self-similarity In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales.
Which is an example of a self similar object?
Standard (trivial) self-similarity. In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales.
What is the definition of a hexagon in English?
English Language Learners Definition of hexagon. mathematics : a flat shape that has six angles and six sides. See the full definition for hexagon in the English Language Learners Dictionary.
When does a Koch curve have a self similarity?
A Koch curve has an infinitely repeating self-similarity when it is magnified. Standard (trivial) self-similarity. In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e. the whole has the same shape as one or more of the parts).
