# Manuel Diaz Regueiro

The 3d works of art that I present are intended to show the surprising
and amazing results that are achieved using mathematics, computer
programs elaborated for this purpose and professional 3D printers.

As Galileo said: "Philosophy (and Art) is written in this grand book -
I mean universe - which stands continuously open to our gaze, but
which cannot be understood unless one first learns to comprehend the
language in which it is written. It is written in the language of
mathematics, and its characters are triangles, circles and other
geometric figures... "

This time what I use are circles to represent Tornado's cup, equations
for Typhoons and L-Systems for Granada.

My first encounter with tornadoes in mathematics took place in
1982, in a course of UMI in Cortona (Arezzo), taught by Dr.
Serrin. The present work now reminds tornadoes and typhoons that
are created with air masses in circular or elliptical rotations in
the z axis and at an angle or shear. The image looks like a torus,
but it is not, its fibers touch at one point, inclined with
respect to the plane of the torus.

The cup: here merely suggested by curves, is defining an open cup
inside, and therefore there are certain types of cups that are
generated by circles. Do you know all the surfaces generated by
circles?

On the other hand, it is possible to see a tornado in equation
form. There are infinite possible unbelievable and beautiful
three-dimensional curves and some of them are approximations of
natural phenomena such as tornadoes or magnetic fields. The fact
of finding partial differential equations that fit could help to
easily find control methods.

This is a representation of a curve with parametric equations with
sines and cosines and, as happens in a phenomenon governed by
these equations, it has a nuclear point at the junction of the
different curves that compose it. We can also see the shape of a
cup suggested in this artwork, drawn with elements extracted from
the curves.

This artwork, created in Granada in the summer of 2013, turns out
to be full of Islamic stars, located at the end of each of the
fourteen towers that follow so many directions in space. It raises
more questions than answers: Why fourteen towers and not twelve?
Why the towers? Why Islamic stars? What is the relationship
between the L-system equations and the result product?

Certainly I do not know, what I can tell is that these problems
are related to the theme of the book of Adrian Bejan "Design in
Nature", in which it is said that everything in the Universe is
governed by dynamical Flow Laws, like the trees. In short,
L-systems are in the midst of more mysteries than an artwork.