Posts Tagged 'Fractals'

Fractal Complexity of Finnegans Wake

Tomorrow we celebrate Bloomsday, the day of action in Ulysses. Most of us regard Joyce’s singular book as a masterpiece, even if we have not read it. In contrast, Finnegans Wake is considered by some as a work of exceptional genius, by others as impenetrable bafflegab [See TM117 or search for “thatsmaths” at irishtimes.com].

FW-Fractals-03-Squeezed.jpg

Wavelet transform of sentence length sequence in Ulysses. Note the structural change around sentence number 13,000. Image from Drozdz, et al (2016).

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The Power Tower Fractal

We can construct a beautiful fractal set by defining an operation of iterating exponentials and applying it to the numbers in the complex plane. The operation is tetration and the fractal is called the power tower fractal or sometimes the tetration fractal. A detail of the set is shown in the figure here.

PTF7

Detail of the power tower fractal.

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Santa’s Fractal Journey

The article in this week’s That’s Maths column in the Irish Times ( TM035 ) is about the remarkable Christmas Eve journey of Santa Claus.

Santa-and-Moon

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Ireland’s Fractal Coastline

Reports of the length of Ireland’s coastline vary widely. The World Factbook of the Central Intelligence Agency gives a length of 1448 km. The Ordnance Survey of Ireland has a value of 3,171 km (http://www.osi.ie). The World Resources Institute, using data from the United States Defense Mapping Agency, gives 6,347km (see Wikipedia article [3]).

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