What math is needed for fractals?

Question

Mathematics

Tell me, please, what sections of mathematics are needed to understand the mathematics of fractals?
Preferably from start to finish
By understanding, I mean free reading, mental solution and the ability to translate into code with the appropriate programming skills, that is, an understanding of the principle of operation

Answer 1

For starters, enough arithmetic. Curves of Peano, Sierpinski and others do not require any special knowledge for repetition
. The next level is Complex Analysis. Knowledge from it is needed to operate with the Joliat set and other iterative pictures and attractors.
With further deepening, higher algebra, topology, number theory, partial differential equations, stability theory, automatic control theory, and so on can be pulled.