# What is statistically self-similar?

## What is statistically self-similar?

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 does the term self-similar mean?

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 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 a self-similar fractal?

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.

### What is an example of self-similarity?

More generally, we know that many objects found in nature have a kind of self-similarity; small pieces of them look similar to the whole. Some examples are clouds, waves, ferns and cauliflowers. We call these objects fractal-like.

### 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 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 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. An example of a self-similar object is the Sierpenski triangle show below.

#### 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 do you mean by similarity solution?

Page 1. B Similarity solutions. Similarity solutions to PDEs are solutions which depend on certain groupings of the independent variables, rather than on each variable separately.

What is self-similar structure?

[ sĕlf′sĭm′ə-lăr′ĭ-tē ] 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.