## Volume 25, Number 3 (2016)

**Segregation Landscape: A New View on the Schelling Segregation Space**

Philippe Collard and Teodor Ghetiu

Thomas C. Schelling showed that global aggregation may occur, even if it does not correspond to agent preferences; thus, to some extent his model supported the view that segregation is unavoidable, whatever the tolerance is. The segregation landscape approach proposed in this paper is seriously weakening this hypothesis; here, we radically change the perspective and propose using the landscape metaphor to represent emergent segregated communities. A segregation landscape is a mapping from situated individuals into an extra dimension that represents the degree of segregation of everyone. This paper uncovers how to interpret hills and valleys, and whether these interpretations are congruent with the intuitive notion of frontier. Such a representation allows us to describe both the static properties of a segregation space and their impact on how information propagates between segregated communities. In order to assess the explanatory power of the landscape metaphor, we devise agent-based simulations. First, we establish the link between the micro-level quantified by individual tolerance and the macro-structure represented by the landscape, then we show how "geographic" properties impact the dynamical behavior on such a population landscape.

**Phenomenology of Tensor Modulation in Elementary Kinetic Automata**

Yuri V. Shalygo

This paper continues and extends the earlier works by the author on a novel model of a complex dynamical system called a kinetic automaton. The primary goal of the paper is to introduce an alternative tensor-based method of modulation and to demonstrate that it not only significantly enhances the tunability of the model and the complexity of its behavior, but also is able to emulate many other discrete-time continuous-state dynamical systems. The paper provides the results of the investigation of spatio-temporal patterns arising under different modes or parameters of modulation in elementary (one-dimensional) kinetic automata. Special attention is given to quantity conservation, which is the most salient feature of the model.

**Distance Distribution between Complex Network Nodes in Hyperbolic Space**

Gregorio Alanis-Lobato and Miguel A. Andrade-Navarro

In the emerging field of network science, a recent model proposes that a hyperbolic geometry underlies the network representation of complex systems, shaping their topology and being responsible for their signature features: scale invariance and strong clustering. Under this model of network formation, points representing system components are placed in a hyperbolic circle and connected if the distance between them is below a certain threshold. Then the aforementioned properties come out naturally, as a direct consequence of the geometric principles of the hyperbolic space containing the network. With the aim of providing insights into the stochastic processes behind the structure of complex networks constructed with this model, the probability density for the approximate hyperbolic distance between *N* points, distributed quasi-uniformly at random in a disk of radius *R*~ln *N*, is determined in this paper, together with other density functions needed to derive this result.

**On Half-Adders Based on Fusion of Signal Carriers: Excitation, Fluidics, and Electricity**

Andrew Adamatzky

Likely outcomes of a collision between two objects are annihilation, reflection, or fusion. We show how to construct a one-bit adder with patterns that fuse on impact. A fusion gate has two inputs and three outputs. When a signal is generated on a single input, the object propagates along its own output trajectory. When both inputs are active, the objects collide at a junction of input trajectories, fuse, and propagate along a dedicated output trajectory. Thus two outputs produce conjunction of one signal with negation of another signal, and the third output produces conjunction of input signals. By merging two outputs in one, we make a one-bit half-adder: one output is the conjunction of input signals; another output is the exclusive disjunction of the signals. We discuss blueprints of the half-adders realized with two types of physical signal carriers—wave fragments in excitable medium- and high-velocity jet streams. We also propose an electrical circuit analogous to a fusion half-adder. By running fusion half-adders in reverse, we find that despite realizing the same functions when in a straight mode, all devices implement different functions when their inputs are swapped with outputs.

*Complex Systems* ISSN 0891-2513

© 1987–2016

Complex Systems Publication, Inc.

Published four times annually

Complex Systems Publications, Inc.

P.O. Box 6149

Champaign, IL 61826 USA

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