Monday, January 13, 2014

In the appendix of the paper I reference below is a summary derivation of the relationship  between entropy and fractals (power laws). The appendix is also posted in another blog, Plate Frames. The introduction to the post reads...
In a paper published a couple of years ago (Pilger, 2012), I describe the application of a simple principle, transformed into a distinctive abstract object, to an optimization problem (within the plate tectonics paradigm): simultaneous reconstruction of lithospheric plates for a range of ages from marine geophysical data . It is rare that the relation of the principle, maximum entropy, with a particular transformation, power-series fractals, is recognized, since Pastor-Satorras and Wagensberg derived it. I'm unaware of any other application of fractal forms to optimization problems analogous to the paper. The following derivation is taken from the 2012 paper, with slight modification, in hopes that it might prove useful in other fields, not merely the earth sciences, but beyond. I'm investigating  applications in a variety of other areas, from plate tectonics, to petroleum geology, and, oddly enough, the arts.
Pilger, R. H., Jr. (2012) Fractal Plate Reconstructions with Spreading Asymmetry, Marine Geophysical  Research, Volume 33, 149-168. dx.doi.org/10.1007/s11001-012-9152-6. (rexpilger (at) gmail (dot) com.)

Thursday, December 05, 2013

My sister-in-law keeps posting photos whose beauty comes, in part, from fractal structure (a site with other examples of fractal art, natural or human-made). 

Here is her latest example:

Wednesday, December 22, 2010

Fractals and Plate Tectonics

Can fractal criteria be used in deriving plate reconstructions of asymmetrically spreading ridges? See: link.


Before:
After:

Wednesday, November 17, 2010

Peer Review

An article in Physics World describes an "experiment" in peer review and its effect on the quality of published scientific research.
Just a small number of bad referees can significantly undermine the ability of the peer-review system to select the best scientific papers. That is according to a pair of complex systems researchers in Austria who have modelled an academic publishing system and showed that human foibles can have a dramatic effect on the quality of published science.

Monday, November 08, 2010

Jane and Will

Fractal calculations of Jane Austen's six novels imply an unsurprisingly common vocabulary pool. But, what about comparisons with other English literature? Hamlet:

And adding to the Jane Austen plot:

(Click to enlarge; click again to zoom; backspace to return to this post.)

Hamlet and company occupied a smaller "area" in their dramatic fractal space, but note that the slope of the main part of the fractal plot is essentially the same as Jane's novels.

What does it all mean?



Jane Austen

Word frequency usage often shows a logarithmic pattern (e.g., Zipf's distribution). What about fractals? (Click to enlarge graphics; backspace to return to this blog post.)














I suppose one might assume that Jane Austen would draw on the same vocabulary in each novel. How similar are these relationships among the six?

 
The similarity in slopes of the six curves suggests that common vocabulary.

Citation Fractals

Following a suggestion by Murray (2002), I've looked at the indexes of a number of recent scientific monographs and popular scientific accounts and calculated their fractal measures.


Murray combined a large number of text references and normalized them. Applying fractal binning to his results produces:

E. T. Jaynes (2002) Probability Theory:




W. Isaacson (2008) Einstein: His Life and Universe:




L. Gilder (2009) The Age of Entanglement:



S. Pinker (2003) The Blank Slate:




W. Grandy (2008) Entropy and the Time Evolution of Macroscopic Systems: