Fractal Study Page

When I first arrived at the University of Texas at Arlington, I was able to work on a study that attempted to use the idea of fractal dimensions to study high energy particle physics events that undergo hadronization to try to find the root s-hat of the event.

The idea motivating the study was that hadronization appears to be a self-similar process. When dealing with self-similar processes, the idea of fractal dimensions can be very useful.

What we tried to do in this study, was to use monte-carlo data of jet events in a toy calorimeter to study various fractal measures. We used the Hausdorff box counting method, the correlation integral and information entropy methods.

We used both isajet and herwig monte-carlo data since they construct the event (especially the underlying event) differently. One just throws an additional underlying event over the jets while the other attempts to be faithful to the self-similar nature of hadronization. This way we could study any discriminatory nature of the fractal dimensions.


Tasks Deadlines
Write Code 1999 (done)
Generate Plots 1999
Publish 2000


Write Code

The first thing I had to do, was write the code that actually performed the work. This entailed writing various subroutines in c++ (I had to learn this at the time), as well as including fortran calls so I could access the CERNLIB HBOOK utilities. The montecarlo data was processed through a wrapper package written by someone else and then the output of that package was passed through mine.

The packages written include the Hausdorff Box Counting method both in 2 and 3 dimensions, the Correlation Integral method in 2 and 3 dimensions, The Information Entropy method (standard) in 2 and 3 dimensions and a new Information Entropy method (HEP) in 2 dimensions that is a modification of the standard method but including information of interest in High Energy Physics.

I also wrote some packages to generate random data sets as well as a sierpinski data set to test the code and verify that the proper dimensions would be returned.

Status

Generate Plots

The next task was to use the information from the code that I wrote, and then generate some plots an study the results. This was done using PAW and HBOOK routines to fill an ntuple with the data.

Status

Publish

After the study was concluded, the paper was written up for submission to Phys. Rev. D but before it could complete the referee process my advisor left the field. I no longer have contact with the other collaborators and have yet to try to get the paper bublished.

Status


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If you have any questions or comments, please mail me at: strang@fnal.gov

This page last updated: 03-Jun-2001 03:45 AM (UTC -05:00)