Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers

The paper considers a new type of objects - blinking fractals - that are not covered by traditional theories studying dynamics of self-similarity processes. It is shown that the new approach allows one to give various quantitative characteristics of the newly introduced and traditional fractals using infinite and infinitesimal numbers proposed recently. In this connection, the problem of the mathematical modelling of continuity is discussed in detail. A strong advantage of the introduced computational paradigm consists of its well-marked numerical character and its own instrument - Infinity Computer - able to execute operations with infinite and infinitesimal numbers.