Mr. Lauge Koch

Computability of Koch Curve and Koch Island

Koch curve is known as a typical self-similar set on Euclidean plane. Koch island is a closed set surrounded by three copies of Koch curve. We investigate them from the viewpoint of computability. In this paper, we define computability of a curve and that of a closed set as an application of classical computable analisys to Euclidean spaces and show that Koch curve is a computable curve and bot...

Robert Koch

Classification and Diagnosis Lauge-Hansen Classification and Weber’s classification

Lauge-Hansen Classification and Weber’s classification The Lauge-Hansen classification system is based on a rotational mechanism was applied to the ankle in one of three different directions. For a given foot position and deforming force at the ankle, a consistently reproducible pattern of osseous and ligamentous injury was described. The first part of the name in the classification system desc...

Superior Koch Curve

In this paper, the author presents the design of Superior Koch Curve with different scaling factor, which has wide applications in Fractals Graphics. The proposed curve has been designed using the technique of superior iteration. The Koch curve is the limiting curve obtained by applying the self similar divisions to infinite number of times but in Superior Koch Curve scaling factor is based on ...

When Thue-morse Meets Koch

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences an...