Hausdorff dimension

Minkowski–Bouligand dimension

Pure mathematics

Dimension (graph theory)

Computer science

Interpolation (computer graphics)

Lipschitz continuity

Fractal

Mathematics

Image (mathematics)

Fractal dimension

Mathematical analysis

Artificial intelligence

Geometry

Fractal analysis

Fractal derivative

Fractal dimension on networks

Multifractal system

Regular polygon

Bulletin of the Australian Mathematical Society

Based on the work of Mauldin and Williams [‘On the Hausdorff dimension of some graphs’, Trans. Amer. Math. Soc. 298 (2) (1986), 793–803] on convex Lipschitz functions, we prove that fractal interpolation functions belong to the space of convex Lipschitz functions under certain conditions. Using this, we obtain some dimension results for fractal functions. We also give some bounds on the fractal dimension of fractal functions with the help of oscillation spaces.

ON FRACTAL DIMENSIONS OF FRACTAL FUNCTIONS USING FUNCTION SPACES