# Manuel Diaz Regueiro

I have found rules that are appropriate and very productive for lsystem both in 2D and 3D. These are the first steps of my interest in the production of art with mathematical forms. My 3d art is currently formed by a set of several hundred figures, most of them “wire sculptures” with axial symmetry that give place to abstract and beautiful objects. Finding the rules that govern objects and beauty is one of my goals. To find the order and beauty in the complexity rules, one of my hobbies.

In this occasion the theme is about the 3d pursuit curves and lsystems
that are represented in the three examples:

In
www.shapeways.com/shops/regueiro
you can have a look at them or buy some of this type of 3d printer
works, specially some curves of persecution made by all kind of
possible variants and a hundred of 3d lsystems.

What’s the reason why the result of many lsystem that I work with
appear to be ordered? During several years I have been thinking
about the reason. Emergence was the answer. We have a complex
system with a set of gramatical rules and a set of 3d angles. With
certain rules and certain angles, it’s almost compulsory to obtain
a necesary and ordered result, that indicates the existence of a
set of implicit 3d positional theorems that are not described or
are very difficult to be described.

The most amazing thing of these results is that the figure 3d that
you get seems to have intentionality. It is as if you had passed
several months thinking about its final details and had studied
structure to do such a delicate and recognizable object. Something
like a Belousov- Zhabotinsky reaction but with a abstract
gramatical, and not chemical, origin.

We are in presence of the birth of the emergence of order.

For some people it may not be very orthodox to use a public
tragedy like Hurricane Sandy to identify a workart, but what I am
trying to show is that persecution curves in three dimensions
correspond to physical objects that we know and recognize as
hurricanes, spiral galaxies, or even the drain of your bathtub and
that all of them obey the same laws, the Coriolis Effect.

Thus I find that this artwork suggest that there exists the
possibility of governing hurricanes modelling them as prosecution
curves in three dimensions. In these examples the lines are traced
over the edges of platonic solids.

This object is created with a computer program and, by just
varying some elements of it, other similar 3d objects may be born
to light. If the program, that is based in 3d persecution curves,
is able to visualize the physical phenomenon, that means that
these curves will be basic for a model capable to interpret and
control these phenomena. There it goes an interesting mathematical
problem.

Pursuit curves or persecution curves are in the logo of Bridges
Pécs 2010. Several mathematical newsletters use this curve as
logo. What do if translate this curve to three dimensions?

With two perpendicular planes in his definition, letting add
several (two or four) figures to form a pyramid or a
octahedron.

With his characteristics four logarithmic spirals.

I propose this figure like the Enschede Bridges Logo.