FUNDAMENTAL PHYSICS // OPTICAL and LASER FEEDBACK

SPACE-TIME DYNAMICS IN VIDEO FEEDBACK Physica, 1984 James P. Crutchfield

Video feedback provides a readily available experimental system to study complex spatial and temporal dynamics. This article outlines the use and modeling of video feedback systems. It includes a discussion of video physics and proposes two models for video feedback dynamics based on a discrete-time iterated functional equation and on a reaction-diffusion partial differential equation. Color photographs illustrate results from actual video experiments. Digital computer simulations of the models reproduce the basic spatio-temporal dynamics found in the experiments.

FRACTAL EVOLUTION OF NORMALIZED FEEDBACK SYSTEMS ON A LATTICE Siegfried Fussy Gerhard Gr¨ossing Austrian Institute for Nonlinear Studies, Parkgasse 9, A-1030 Vienna, Austria84

Abstract
Highly nonlinear behaviour of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employ ing quantum cellular automata [1] or their real-valued analogues. It is shown that the combination of two operations, i.e. i) enhancement of a site’s value when fulfilling a feedback condition and ii) normalization of the system after each time step, produces relatively short-lived spatiotemporal patterns whose mean lifetime can be considered as emergent order parameter of the system. This mean lifetime obeys a scaling law involving a control parameter which tunes the “fault tolerance” of the feed- back condition. Thus, within appropriate ranges of the systems variables, the dynamical properties can be characterized by a “fractal evolution di- mension” (as opposed to a “fractal dimension”).

Farey sequences of spatiotemporal patterns in video feedback B. Essevaz-Roulet,1 P. Petitjeans,1 M. Rosen,2 and J. E. Wesfreid1

Abstract
In this paper we present an experimental and theoretical description of the dynamic of spatial patterns obtained in a video feedback loop. A video camera monitors the screen to which it is connected and can turn around its optical axis at an angle a. Under certain conditions of brightness and magnification, this optoelectronic system produces spatiotemporal patterns in the form of spots located on a circle on the screen. These patterns are very similar to the spatial transverse modes obtained in other optical devices such as lasers or photorefractive media. It is possible to generate stationary patterns of n-fold symmetries for angles a 52p/n. When the angle a varies around 2p/n, the pattern rotates with a certain frequency proportional to the difference between 2p/n and a. We discover more general patterns at angles 2p/(p/k) with p-fold symmetry, following the hierarchy of the Farey algorithm which theoretically can produce stationary patterns at any angle a. Very accurate experiments were performed to observe these patterns up to the level k56. This is the first time a Farey tree has been observed as a sequence of spatial patterns to our knowledge. Previous observations of this hierarchy were made only in the temporal domain.

Dye-doped organic distributed-feedback lasers with index and surface gratings: the role of pump polarization and molecular orientation

Daniel Wright, Etienne Brasselet, and Joseph Zyss // Gregor Langer and Wolfgang Kern Manuscript received September 16, 2003; revised manuscript received December 5, 2003; accepted January 20, 2004

The dependence of the laser threshold of organic distributed-feedback (DFB) lasers having index and surface gratings on the pump polarization angle is studied and examined. A model is developed to describe the relationship between the fluorophore orientational distribution and the number of photons emitted into the laser mode. Experimental data fitted with this model demonstrate that the fluorophores are isotropically oriented in the plane of the sample. The polarization dependence of the laser threshold is then used in conjunction with the measured pump intensity dependence of the emission intensity to explain the pump polarization selectivity of the laser emission of these structures. The effect of the above phenomena on future applications is discussed. © 2004 Optical Society of America

All-optical tunability of holographically multiplexed organic distributed feedback lasers

D. Wright, E. Brasselet and J. Zyss // G. Langer,a A. Pogantsch,b K. F. Iskra,c T. Negerc and W. Kerna


Abstract: We report the fabrication and characterization of optically pumped multiple grating distributed feedback lasers in dye doped organic thin films. Each multiplexed laser structure is inscribed at a different angle in the sample plane and possesses a unique emission wavelength. The polarization sensitivity of these structures with respect to the pumping light is exploited to enable simple and high-speed switching of the device emission wavelength.

FUNDAMENTAL PHYSICS // EVOLUTION FRACTAL and NOISE

A SIMPLE MODEL FOR THE EVOLUTION OF EVOLUTION

Siegfried Fussy, Gerhard Gr¨ossing and Herbert Schwablct

Abstract
A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of fractal evolution which has been shown to constitute a fundamental property of nonlinear discretized systems with one memory- or random-based feedback loop. The latter involves a basic“cognitive” function of each species given by the power of distinction of states within some predefined resolution. The introduction of a realistic background noise limiting the range of the feedback operation yields a pattern signature in fitness space with a distribution of temporal boost/mutation distances according to a randomized devil’s staircase function. Introducing a further level in the hierarchy of the system’s rules, the possibility of an adaptive evolutionary change of the resolution itself is implemented, thereby providing a time-dependent measure of the species’ cognitive abilities: an additional feedback loop makes use of the inevitable intrinsic fluctuations within the fitness landscape to direct the temporal change of the resolution. Feeding back the small adaptive changes of resolution into the essentially directionless variations of the patterns’ lifetimes in fitness space effectively leads to a clear tendency towards increasing evolution potentials for each species (”hierarchically emergent fractal evolution”).

Progressive Evolution and a Measure for its Noise-dependent Complexity

Siegfried Fussy, Gerhard Grössing, and Herbert Schwabl

Abstract
A recently introduced model of macroevoluton is studied on two different levels of systems analysis. Firstly, the systems dynamics and properties, above all the growth of complexity of the evolutionary units during the long-term evolution, are discussed, and, secondly, the complexity of the model itself, i.e. the richness of its various features, is studied with regard to a control parameter representing a background noise within the systems dynamics. The same is done with a randomized version of the model. The model is based on a normalized one-dimensional coupled map lattice with locally interacting sites representing different species. The evolution of the sites' values representing the fitness of the species is governed by a usual diffusion rule and an additional memory- or random-based feedback loop. The introduction of a realistic background noise limiting the range of the feedback operation yields a pattern signature in fitness space with a distribution of temporal boost/mutation distances similar to a punctuated equilibrium behavior. Furthermore, the behavior of the mean lifetimes of ''high'' fitness values is correlated with the resolution-like parameter ε via a power law, a phenomenon called ''fractal evolution''. Based on simple functional properties of the power law, an additional feedback loop is introduced to use the intrinsic fluctuations of the whole fitness landscape as a driving force to change adaptively the systems resolution. On long-term scales, the dynamical system properties exhibit a clear tendency towards progressive evolution potentials for each species. For both model versions, the memory-based and the random-based one, we achieve some basic mechanisms of evolutionary dynamics like coevolution, punctuated equilibrium with regard to internal or external changes during evolution, coordinated stasis for groups of species, and self-organized growth of complexity for all evolutionary units of the array leading to a kind of "Red-Queen-effect" Additionally, for the memory based model a parameter was found indicating a limited range of noise allowing for the most complex behavior of the model, whereas the entropy of the system provides only a monotonous measure with respect to the varying noise level.