Table of a Weierstrass continuous non-differentiable function

Insertion of a gamma-continuous function

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

An Analysis of Katsuura’s Continuous Nowhere Differentiable Function

A Rough Differentiable Function

A real-valued continuously differentiable function f on the unit interval is constructed such that ∞ ∑ k=1 βf (x, 2 −k) = ∞ holds for every x ∈ [0, 1]. Here βf (x, 2−k) measures the distance of f to the best approximating linear function at scale 2−k around x.

A "Superfat" Attractor with a Singular-Continuous 2-D Weierstrass Function in a Cross Section

A 3-D invertible map generating a 4-loop solenoid attractor is presented. The attractor of the "standard" 4-solenoid turns out to be "fat" that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowheredifTerentiab...

Everywhere Continuous Nowhere Differentiable Functions

Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...