Representing fractals by superoscillations
Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any des...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2017-06, Vol.50 (22), p.22 |
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| container_issue | 22 |
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| container_title | Journal of physics. A, Mathematical and theoretical |
| container_volume | 50 |
| creator | Berry, M V Morley-Short, S |
| description | Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 216 are easily represented by superoscillations with fastest Fourier frequency 1. |
| doi_str_mv | 10.1088/1751-8121/aa6fba |
| format | Article |
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| issn | 1751-8113 1751-8121 |
| language | eng |
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| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | approximation band-limited Fourier scaling |
| title | Representing fractals by superoscillations |
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