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- W2484271993 abstract "We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line and circle, showing that it takes the form of the self-similar dimension for a self-similar fractal, with lower bound of 1. Upper bounds to the Hausdorff dimension as functions of $omega$ have been determined for the linear helical fractal, curved helical fractal and circular fractal, based on the no-self-intersection constraint. For large number of windings $omegarightarrowinfty$, the upper bounds all have the limit of 2. This would suggest that carrying out a topological analysis on the structure of chromosomes by modelling it as a two-dimensional surface may be beneficial towards further understanding on the dynamics of DNA packaging." @default.
- W2484271993 created "2016-08-23" @default.
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- W2484271993 date "2013-06-19" @default.
- W2484271993 modified "2023-10-16" @default.
- W2484271993 title "Helicaliser: A formulation of helicalised fractals based on the geometrical properties of the self-similar discrete version" @default.
- W2484271993 hasPublicationYear "2013" @default.
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