Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Micro and Macro Fractals generated by multi-valued dynamical systems   Given a multi-valued function $\Phi$ on a topological space $X$ we study the
properties of its fixed fractal, which is defined as the closure of the orbit
$\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set
$Fix(\Phi)=\{x\in X:x\in\Phi(x)\}$ of fixed points of $\Phi$. A special
attention is paid to the duality between micro-fractals and macro-fractals,
which are fixed fractals for a contracting compact-valued function $\Phi$ on a
complete metric space $X$ and its inverse multi-function $\Phi^{-1}$. With help
of algorithms (described in this paper) we generate various images of
macro-fractals which are dual to some well-known micro-fractals like the
fractal cross, the Sierpinski triangle, Sierpinski carpet, the Koch curve, or
the fractal snowflakes. The obtained images show that macro-fractals have a
large-scale fractal structure, which becomes clearly visible after a suitable
zooming.

26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin