Abstract
AbstractĂąâŹâTwo properties must be available in order to construct a fractal set. The first is the self similarity of the elements. The second is the real fraction number dimension. In this paper, condensation principle is introduced to construct fractal sets. Condensation idea is represented in three types. The first is deduced from rotation ĂąâŹâreflection linear transformation. The second is dealt with group action. The third is represented by graph function.
Highlights
When Mandelbrot started writing about fractals, he came up with the notion that they should be self-similar
We can consider that the iterated function systems (IFS) is the generator of fractal set or shape
This section is concerned of writing the basic mathematical concepts of fractal sets
Summary
When Mandelbrot started writing about fractals, he came up with the notion that they should be self-similar. Our way to formalize is through iterated function systems (IFS) which is due to analogous the dynamical systems They have lots of similar properties, where the name IFS comes from, and reminds us of dynamical systems. Iterated Function Systems (IFS) play a good role for constructing fractal shapes. IFS fractals work by transforming segments of a data set into smaller segments that are self-similar. If. X and applies these maps iteratively , he will come arbitrarily close to a set of points A in X called the attractor of the IFS. X and applies these maps iteratively , he will come arbitrarily close to a set of points A in X called the attractor of the IFS Condensation principle is introduced to construct fractal set of many shapes.
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