Emergence of self-replicating structures in a cellular automata space

Past cellular automata models of self-replication have always been initialized with an original copy of the structure that will replicate, and have been based on a transition function that only works for a single, specific structure. This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components. These emergent self-replicating structures employ a fairly general rule set that can support the replication of structures of different sizes and their growth from smaller to larger ones. This rule set also allows “random” interactions of self-replicating structures with each other and with other structures within the cellular automata space. Systematic simulations show that emergence and growth of replicants occurs often and is essentially independent of the cellular space size, initial random pattern of components, and initial density of components, over a broad range of these parameters. The number of replicants and the total number of components they incorporate generally approach quasi-stable values with time.     

On the origin of self-replicating information-containing polymers from oligomeric mixtures

Within the renormalization group formalism we study condensation reactions between oligomeric molecules catalysed by residues complementary to the growing ones. By assuming that the substrate-catalyst binding constatnt is the relevant parameter, we show that the transition to an information-containing self-replicating polymer is a critical phenomenon.     

Hyperbolic patterns

Hyperbolic patterns constructed basing on higher derivatives of the hyperbolic tangent represent specially designed sums of even powers of soliton-like excitations. Under certain limitations, the hyperbolic patterns satisfy solutions of an equation which is homomorphic to the Klein-Gordon one. Since the hyperbolic patterns may be considered as mathematical images of wave packets, the problem of de Broglie's double solution is discussed. The hyperbolic patterns can be used to construct spatially localized dynamic structures.     

Hidden patterns

Inks of different types are used together to create a radial spread. Then, having been the cause of the spread, the ink also provides the means of visualizing it. Photographic sequences show the progress of the patterns of the spread as they develop. Images are taken from significant points within the sequences, and, bearing in mind aesthetic considerations, are displayed alone or as part of a group.     

Nonequilateral hexagonal patterns

Rotational symmetry of pattern formation problems is the origin of a variety of patterns (rolls, squares, hexagons etc.) in convection and reaction-diffusion systems. Traditionally, only the patterns based on equilateral lattices in the Fourier space were considered. In the present paper, we develop an analysis of the patterns with slightly different lengths of the basic wave vectors. The analysis applies as well to systems with a broken rotational symmetry (convection in an inclined layer, etc.). We find, in the framework of the amplitude equations, existence and stability conditions for periodic nonequilateral patterns based on two and three wave vectors. In the latter case, special attention is paid to the case when the three amplitudes are coupled by the resonant interaction.     

Genetic oscillation patterns

We apply symbolic dynamics to analyze dynamical measurements obtained from gene regulations of cells. Dividing the temporal signals of for instance protein concentrations into regimes of monotonic increasing or decreasing levels gives a natural symbolic division which can be applied to guess the underlying negative feed-back loops. We further study how negative feed-back loops can be placed on a hexagonal lattice and investigate the dynamical consequences of that.     

Complexity of two-dimensional patterns

To describe quantitatively the complexity of two-dimensional patterns we introduce a complexity measure based on a mean information gain. Two types of patterns are studied: geometric ornaments and patterns arising in random sequential adsorption of discs on a plane (RSA). For the geometric ornaments analytical expressions for entropy and complexity measures are presented, while for the RSA patterns these are calculated numerically. We compare the information-gain complexity measure with some alternative measures and show advantages of the former one, as applied to two-dimensional structures. Namely, this does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system. Received 12 November 1999     

Phyllotactic patterns on plants

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces may be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the strain energy is minimized by configurations consisting of special triads of almost periodic deformations. We reproduce a wide spectrum of plant patterns, all with the divergence angles observed in nature, and show how the occurrences of Fibonacci-like sequences and the golden angle are natural consequences.     

Complex spatiotemporal convection patterns

This paper reviews recent efforts to describe complex patterns in isotropic fluids (Rayleigh-Benard convection) as well as in anisotropic liquid crystals (electro-hydrodynamic convection) when driven away from equilibrium. A numerical scheme for solving the full hydrodynamic equations is presented that allows surprisingly well for a detailed comparison with experiments. The approach can also be useful for a systematic construction of models (order parameter equations). (c) 1996 American Institute of Physics.     

Nondiffracting random intensity patterns

We report a simple approach for generating nondiffracting random intensity patterns that do not change with propagation. Experimental results are shown where the generating patterns are encoded onto a phase-only liquid-crystal display. We expect that these results will be useful for encryption or surveillance applications.     

Causodynamics of autowave patterns

Perturbative dynamics of spiral and scroll waves involves the "response functions," i.e., critical eigenvectors of the adjoint linearized operator, dual to the Goldstone modes. A well known method of calculating the Goldstone modes is time integration of the linearized equation. We suggest that backward-time integration of the adjoint linearized equation, which we call causodynamics, can be used to calculate the response functions. This new method is more robust and easier to implement than existing methods. We illustrate how it works for propagating and rotating autowaves in reaction-diffusion systems. The method reveals unexpected qualitative difference between similarly looking regimes.     

Spiral patterns in magnets

An autowave model of the spiral pattern formation in magnets located in a rotating magnetic field is proposed. The model is based on the overdamped double sine-Gordon equation. Nucleation of spiral domains is associated with the averaged motion of domain walls in the rotating field. A vortex-type defect (Bloch line) is the core of the spiral.