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A Mathematical Formula deciphers the geometry of surfaces like that of a cauliflower
What is the research about?
The research was carried out by three institutions
that have worked together for nearly a decade.
Pontifical University of Comillas, Charles III University of Madrid,
and the Institute of Material Sciences (CSIC).
And we are basically interested in describing or portraying surfaces,
both in the CSIC experiments
as well as in making theoretical models, in the case of the Universities,
and how shapes are formed on surfaces.
For the purpose of this experiment,
we are studying hydrogenated carbon surfaces
applying a technique that is highly used in micro-electronics,
that of chemical vapour deposition (CVD) growth.
While studying these properties,
with interests in the application aspect of these kinds of materials,
we quite unexpectedly stumbled upon shapes
that remind us of fractal structures like cauliflowers.
What is the main conclusion of your research?
The main conclusion of our study is that,
analysing the experiments at nanometric scale, on thin films,
it is possible to find a precise description
of evolution in time morphologies with a texture
of the kind from the cauliflower plant family.
Said texture was already known within the scope of nanoscience.
We were able to make experiments
and to re-make them through a theoretical model,
and the interesting thing is that the predictions
of the behaviour of said morphologies at large scales,
are also verified in other very distinct areas.
For example, the cauliflower itself, a plant with which we are familiar,
or other systems like the flame front.
Or in clouds, etc. Or in a whole variety of systems.
What is a fractal and where in the wild can it be found?
Basically, a fractal is a geometric object,
in which, when a part of the system is extended,
it seems like the entire system.
And it appears in all parts of the wild.
Beginning with the shapes of river basins,
up to, for example, the blood system.
In the blood system, it is evident that the vessels at the end
are very much like those in the middle,
- are very much like those an the start.
The power to repeat itself is what depicts a fractal.
How can this study be applied?
Our study can be as much, kind of "conceptually"
as can be concretely applicable.
Concrete applications would mean a better understanding
of the conditions under which the conditions of certain systems
like that of coating, is smoother or rougher.
The conceptual applications would be that of suggesting very general mechanisms
that could be intervening in the formation of these structures
in areas that are very different
from those in which we formulated the model.
Thus, we do think that it may be inspired
on the description of how cauliflowers grow,
judging from very general mechanisms,
like when various parts of the plant compete for resources,
the non-conservation of the material, etc.
(Music)