This paper proposes a new way to classify fractals based on varying of their iteration rules. 1. Static fractals: if the rules never change. 2. Dynamic fractals. And dynamic fractals can be classified as 2.1 dynamic structure fractals (the varying of iterations have certain structures or patterns, like dynamic linear structure fractals, dynamic non-linear structure fractals), and 2.2 dynamic random fractals (some randomness will be introduced into the variation of iteration, like fractals with static structure and randomness, fractals with linear structure and randomness, fractals with non-linear structure and randomness). It also builds a full mathematical model and analysis which introduces the X-fractal basis from the perspective of measure, direction, position, and quantity, based on this classification. Which offer a more clear and intuitive classification, providing a new mathematic framework to analysis fractals. This paper also discuss the Hausdorff dimension and the measure, try to propose a new way to describe the dimension continuity and try to reveal the nature of the continuity and the connections to the symmetry of iterating structures of fractals with a more general concept of entropy symmetry. This is a preprint version.
Lihan Xia (Mon,) studied this question.