Erin P. J. Pearse

A TUBE FORMULA FOR THE KOCH SNOWFLAKE CURVE, WITH APPLICATIONS TO COMPLEX DIMENSIONS

A formula for the interior e-neighbourhood of the classical von Koch snowflake curve is computed in detail. This function of e is shown to match quite closely with earlier predictions from [La-vF1] of what it should be, but is also much more precise. The resulting ‘tube formula’ is expressed in terms of the Fourier coefficients of a suitable nonlinear and periodic analogue of the standard Cantor staircase function and reflects the self-similarity of the Koch curve. As a consequence, the possible complex dimensions of the Koch snowflake are computed explicitly.

Geometry of canonical self-similar tilings

We give several different geometric characterizations of the situation in which the parallel set

Resistance Boundaries of Infinite Networks

F_\epsilon

Minkowski Measurability Results for Self-Similar Tilings and Fractals with Monophase Generators

of a self-similar set

Symmetric Pairs and Self-Adjoint Extensions of Operators, with Applications to Energy Networks

F

Symmetric Pairs of Unbounded Operators in Hilbert Space, and Their Applications in Mathematical Physics

can be described by the inner

Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications

\epsilon

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics

-parallel set

Tube Formulas and Complex Dimensions of Self-Similar Tilings

T_{-\epsilon}

Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

of the associated canonical tiling