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Fractal geometry. (Czech) Zbl 0704.28004
The paper contains a short information about fractals, i.e. about sets whose Hausdorff dimension is higher than their topological dimension. The most simple fractals are self-similar sets, i.e. sets in $$E_ n$$, for which there exist maps $$\phi_ 1,...,\phi_ m:\;E_ n\to E_ n,\quad m\geq 2,$$ such that $$E=\cup^{m}_{i=1}\phi_ i(E),$$ where $$\phi_ i$$ are compositions of isometries and homotheties and where the intersections $$\phi_ i(E)\cap \phi_ j(E)$$ for $$i\neq j$$ are not “too big”. Another example of fractals are Julia’s sets. Let $$f_ c(z)=z^ 2+c,$$ where c is a complex number. The Julia’s set $$J_ c$$ of the function $$f_ c(z)$$ is the boundary of the set of complex numbers z for which the sequence $$f_ c(z),f_ c(f_ c(z)),f_ c(f_ c(f_ c(z))),...$$ is bounded.
Many fractals can be generated by support of computer graphics.
Reviewer: M.Jůza
##### MSC:
 28A80 Fractals 28A78 Hausdorff and packing measures