Fractal-Dimension Books

This book introduces a new emerging field of inquiry and is a coherent overview of this important new subject. It presents concrete detail within a more general framework. The book introduces the cross disciplinary question: how does one use dimension theory(mathematics) to study the dynamics of a system(physics). How does one, for example, correlate the structure of an attractor seen as dimension with entropy and Lyapunov exponents? The book is current and in places exciting.

Dimension theory is related in deep ways to the dynamical parameters affecting the dimension of an invariant set. The main parameters are the characteristic contraction rates of the dynamics which have resulted in a large number of definitions of dimension (Hausdorf, box, Besicovich, correlation, and information dimensions). These definitions agree with each other when they take integer values but may not agree always.

A primary issue has been to estimate the fractal dimension of invariant sets of dynamical systems. This book provides a deep understanding of the many useful dimensional characteristics and tells how to compute these. Pesin takes his notions of dimension from one concept which unifies his approach. The book begins with generalities concerning the characteristics of dimension, sets and measures, building upon the Caratheodory construction. Pesin then applies a metric to the space to allow the Hausdorf and box dimensions to emerge as specific cases. Pesin then applies these to dimension theory within the context of dynamical systems.

Pesin then using a dynamical system approach develops a thermodynamical formalism obtaining useful dimensional definitions of topological and metric entropy and topological pressure.

The latter portion of the book uses the theory within the context of hyperbolic invariant sets and measures.

Those studying fractal invariant sets of dynamical systems will enjoy this book.

It is rare to find something that manages a new take on an old paradigm, but this is just what the System of Role Development is doing for pen and paper role-playing game mechanics. While the system obviously has its roots firmly in the AD&D era of games, it must have moved in very different directions since its conception. Unlike many newer games, SORD is not afraid to try and simulate reality with numbers rather than theatrical guidelines, making it very useful for realistic game worlds. Of course, if you don't like that, you can always rip sections of the rules out -- SORD is gratifyingly modular, if not as deliberately so as FUDGE.

The principal and obvious difference between SORD and other mechanistic games is that it is "formula driven." What this appears to mean is that all of the complex (I'd rate SORD around 3 on a scale of 1-5 in complexity, with Aria or Rolemaster sitting at 5 or so) aspects of the game mechanics are dealt with outside of ga! ! me play, during character creation or that time you spend sitting around chatting before the game begins. For example, SORD follows the example of Phoenix Command in that parts of a character's combat effectiveness depends on the weight carried. Unlike Phoenix Command, however, SORD plays very fast (even with inexperienced players) because all aspects of a character are rendered down to a single target for a d20 roll for any given task.

But obviously, I don't have room to talk extensively about mechanics. I'll just mention the elegant way in which weapons are treated (which I have already stolen for another game in a different system), and the sensible way in which setting-specific rules areas are entirely devolved to the settings themselves. Oh yes, and the abstract damage system works wonderfully well for an abstract damage system...you get a very good feel for how your character is *feeling* as a fight progresses.

Setting-wise, SORD comes with a gritty yet romantic Robi! ! n Hood "mini-setting" in which medieval England i! s a harsh place for the poor to survive. Many of the rules are contained within this setting, as skills, professions, weapons, armor, etc, are all setting-specific. (But this set is general enough to provide a good starting point for any low-fantasy or historical setting).

In summary, definately worth a look, and beats the pants off GURPS and Rolemaster for mechanics -- now we just have to wait for Fractal Dimensions to bring out some cool settings...

As a final note, the System of Role Development has extensive -- and free -- online resources available, including a number of settings and rule guides. A URL is given in the book -- a welcome trend for those of us who like to get more than we pay for.