What is difference between self-similar and strictly self-similar?

If parts of a figure are small replicas of the whole, then the figure is called self-similar…. A figure is strictly self-similar if the figure can be decomposed into parts which are exact replicas of the whole.

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.

What is an example of self-similarity?

An example of a self-similar object is the Sierpenski triangle show below. As one looks closer we observe that the large triangle is composed of three smaller triangles half the size (side length) of the original, which in turn are composed of three smaller triangles, and so on, and so on.

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.

Is the Koch snowflake self-similar?

The Koch snowflake is among the earliest fractal geometry work. Not surprisingly, nature’s snowflakes seem to share that self similarity the Swedish mathematician Helge von Koch described.

What is a self-similar flow?

In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled.

What is self affine surface?

Self-affine is a kind of self-similarity, where the scaling is different in each of the axis. Self-similar objects on the other hand grow at the same magnification factor in all three axis in same time frame. Thus, a self-affine object changes as we zoom in, unlike a self-similar object.

What’s another word for similarity?

Some common synonyms of similarity are analogy, likeness, resemblance, and similitude.

Is a hexagon 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.

Is the perimeter of snowflake island infinite?

times the area of the original triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite perimeter.

Why do fractals have infinite perimeter?

The perimeter is not the number of sides, it is the sum of the lengths of the sides. And it is possible for a sum of an infinite number of positive terms to be finite. But it is not only wrong, it is irrelevant, because fractals don’t have any “sides” (straight segments on their perimeter) at all.

What is self similarity in turbulence?

A turbulent flow is said to be self-similar when some or all of its statistical properties depend only on certain combi- nations of the independent variables rather than on each in- dependent variable individually.

What is a more general notion than self-similarity?

A more general notion than self-similarity is Self-affinity . The Mandelbrot set is also self-similar around Misiurewicz points . Self-similarity has important consequences for the design of computer networks, as typical network traffic has self-similar properties.

What is self similarity in physics?

Self-similarity. It happens if the quantity exhibits dynamic scaling. The idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the numerical values of their sides are different however the corresponding dimensionless quantities, such as their angles, coincide.

What is the difference between scale invariance and self similarity?

Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole.

What is the meaning of self similar in music?

In music. In the research field of music information retrieval, self-similarity commonly refers to the fact that music often consists of parts that are repeated in time. In other words, music is self-similar under temporal translation, rather than (or in addition to) under scaling.