Analysis of fractal groups of the type d-(m,r)-Cantord-(m,r)-Cantor within the framework of Kaniadakis statistics

•We analyze the entropy of a generalized Cantor set within a Kaniadakis framework.•The block entropy in this context is obtained for a set of sample sizes.•We found a value of the entropic parameter (κ), which makes the entropy linear.•A linear entropy increasing indicates a non-fractal growth with sample size.•The entropy associated with these structures also shows power-law type behavior.

We have used Kaniadakis statistics in the analysis of fractal structures of the type d-(m,r)-Cantord-(m,r)-Cantor. The κ-entropy associated with these structures shows linearity with respect to the dimension L of the system and power-law type behavior with respect to the block size s   used in the scanning of a determined sequence. The fractal dimension dfdf is related to the entropic parameter κ through an inverse-type law.