Archive for the ‘Fractals’ Category

Introduction to Complexity course is now enrolling!

Tuesday, February 5th, 2013

Santa Fe Institute’s Introduction to Complexity course is now enrolling!

From the webpage:

This free online course is open to anyone, and has no prerequisites. Watch the Intro Video to learn what this course is about and how to take it. Enroll to sign up, and you can start the course immediately. See the Syllabus and the Frequently Asked Questions to learn more.

I am waiting for the confirmation email now.

Definitely worth your attention.

Not that I think subject identity is fractal in nature.

Fractals as you know have a self-similarity property and at least in my view, subject identity does not.

As you explore a subject identity, you encounter other subjects identities, which isn’t the same thing as being self-similar.

Or should I say you will encounter complexities of subject identities?

Like all social constructs, identification of a subject is simple because we have chosen to view it that way.

Are you ready to look beyond our usual assumptions?

Update: Introduction to Complexity [Santa Fe Institute]

Wednesday, December 5th, 2012

The Santa Fe Institute has released the FAQ and syllabus for its “Introduction to Complexity” course in 2013.

The course starts January 28, 2013 and will last for eleven (11) weeks.

Lecture units:

  1. What is Complexity?
  2. Dynamics, Chaos, and Fractals
  3. Information, Order, and Randomness
  4. Cellular Automata
  5. Genetic Algorithms
  6. Self-Organization in Nature
  7. Modeling Social Systems
  8. Networks
  9. Scaling
  10. Cities as Complex Systems
  11. Course Field Trip; Final Exam

Funding permitting there may be a Complexity part II in the summer of 2013.

Your interest and participation in this course may help drive the appearance of the second course.

An earlier post on the course: Introduction to Complexity [Santa Fe Institute].

MongoDB Index Shootout: Covered Indexes vs. Clustered Fractal Tree Indexes

Friday, September 7th, 2012

MongoDB Index Shootout: Covered Indexes vs. Clustered Fractal Tree Indexes by Tim Callaghan.

From the post:

In my two previous blogs I wrote about our implementation of Fractal Tree Indexes on MongoDB, showing a 10x insertion performance increase and a 268x query performance increase. MongoDB’s covered indexes can provide some performance benefits over a regular MongoDB index, as they reduce the amount of IO required to satisfy certain queries. In essence, when all of the fields you are requesting are present in the index key, then MongoDB does not have to go back to the main storage heap to retrieve anything. My benchmark results are further down in this write-up, but first I’d like to compare MongoDB’s Covered Indexes with Tokutek’s Clustered Fractal Tree Indexes.

MongoDB Covered Indexes Tokutek Clustered Fractal Tree Indexes
Query Efficiency Improved when all requested fields are part of index key Always improved, all non-keyed fields are stored in the index
Index Size Data is not compressed Generally 10x to 20x compression, user selects zlib, quicklz, or lzma. Note that non-clustered indexes are compressed as well.
Planning/Maintenance Index “covers” a fixed set of fields, adding a new field to an existing covered index requires a drop and recreate of the index. None, all fields in the document are always available in the index.

When putting my ideas together for the above table it struck me that covered indexes are really about a well defined schema, yet NoSQL is often thought of as “schema-less”. If you have a very large MongoDB collection and add a new field that you want covered by an existing index, the drop and recreate process will take a long time. On the other hand, a clustered Fractal Tree Index will automatically include this new field so there is no need to drop/recreate unless you need the field to be part of a .find() operation itself.

If you have some time to experiment this weekend, more MongoDB benchmarks/improvements to consider.

Fractals in Science, Engineering and Finance (Roughness and Beauty)

Saturday, January 7th, 2012

Fractals in Science, Engineering and Finance (Roughness and Beauty) by Benoit B. Mandelbrot.

About the lecture:

Roughness is ubiquitous and a major sensory input of Man. The first step to measure and simulate it was provided by fractal geometry. Illustrative examples will be drawn from the sciences, engineering (the internet) and (more extensively) the variation of financial prices. The beauty of fractals, an unanticipated “premium,” helps in teaching and bridges some chasms between different aspects of knowing and feeling.

Mandelbrot summaries his career as the pursuit of a theory of roughness.

Discusses the use of the eye as well as the ear in discovery (which I would call identification) of phenomena.

Have you listened to one of your subject identifications lately?

Are subject identifications rough? Or are they the smoothing of roughness?

Do your subjects have self-similarity?

Definitely worth your time.

First seen at: Benoît B. Mandelbrot: Fractals in Science, Engineering and Finance (Roughness and Beauty) over at Computational Legal Studies.