7 citations · 16 across the 9 of their papers we have counts for
9 papers
On the revolving structure of the Lévy dragon and its linear transforms
Miguel Gonzalez-Carriedo, Kiko Kawamura, Jonathan Leung +1
Lévy's Dragon Curve is a well-known self-similar fractal, notable for its ability to tile the complex plane. We review a representation of the curve as a set of points given by com…
The higher order partial derivatives of Okamoto's function with respect to the parameter
Pieter Allaart, Nathan Dalaklis, Kiko Kawamura +2
Let be Okamoto's family of continuous self-affine functions, introduced in [{\em Proc. Japan Acad. Ser. A Math. Sci.} {\bf 81} (2005), no. 3, 47--50]. This fam…
-revolving sequences and self-similar sets in the plane
Kiko Kawamura, Tobey Mathis
Initiated by Mizutani and Ito's work in 1987, Kawamura and Allen recently showed that certain self-similar sets generalized by two similar contractions have a natural complex power…
The partial derivative of Okamoto's functions with respect to the parameter
Nathan Dalaklis, Kiko Kawamura, Tobey Mathis +1
The differentiability of the one parameter family of Okomoto's functions as functions of has been analyzed extensively since their introduction in 2005. As an analogue to a sim…
Revolving sequences and Terdragon
Tobey Mathis, Kiko Kawamura
In 1970, Davis and Knuth introduced the concept of revolving sequences to represent Gaussian integers. Much later, Kawamura and Allen recently generalized this idea to a wider clas…
Revolving Fractals
Kiko Kawamura, Andrew Allen
Davis and Knuth in 1970 introduced the notion of revolving sequences, as representations of a Gaussian integer. Later, Mizutani and Ito pointed out a close relationship between a s…
The Takagi function: a survey
Pieter Allaart, Kiko Kawamura
This paper sketches the history of the Takagi function T and surveys known properties of T, including its nowhere-differentiability, modulus of continuity, graphical properties and…
At which points exactly has Lebesgue's singular function the derivative zero ?
Kiko Kawamura
Let L_a(x) be Lebesgue's singular function with a real parameter a (0<a<1, a not equal to 1/2). As is well known, L_a(x) is strictly increasing and has a derivative equal to zero a…
The improper infinite derivatives of Takagi's nowhere-differentiable function
Pieter C. Allaart, Kiko Kawamura
Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono, we give a complete characterization of those…