## Volume 25, Number 2 (2016)

**Predicting the Large-Scale Evolution of Tag Systems**

Carlos Martin

We present a method for predicting the large-scale evolution of a tag system from its production rules. The tag system's evolution is divided into stages called "epochs" in which the tag system evolves monotonously. The distribution of strings of symbols in the queue at the beginning of an epoch determines the large-scale behavior of the tag system during that epoch, including its growth rate. To predict the tag system's large-scale properties over multiple epochs, we show how to predict the next epoch's initial queue contents from the current epoch's initial queue contents. We compare the values predicted by this method to simulations and find that great prediction accuracy is retained over several epochs.

**A Glimpse of the Mandelbulb with Memory**

Ramón Alonso-Sanz

An exploratory study is made concerning the effect of memory of past states on the dynamics of a kind of triplex number iterative map. Particular attention is paid to the case of the map generating the so-called Mandelbulb set.

**On Complexity of Persian Orthography: L-Systems Approach**

Nassim Taghipour, Hamid Haj Seyyed Javadi, Mohammad Mahdi Dehshibi, and Andrew Adamatzky

To understand how the Persian language developed over time, we uncover the dynamics of complexity of Persian orthography. We represent Persian words by L-systems and calculate complexity measures of these generative systems. The complexity measures include degrees of non-constructability, generative complexity, and morphological richness; the measures are augmented with time series analysis. The measures are used in a comparative analysis of four representative poets: Rudaki (858–940 AD), Rumi (1207–1273), Sohrab (1928–1980), and Yas (1982–present). We find that irregularity of the Persian language, as characterized by the complexity measures of L-systems representing the words, increases over temporal evolution of the language.

**Interaction Strength Is Key to Persistence of Complex Mutualistic Networks**

Wei Su and Lei Guo

The relationship between stability of complex ecosystems and the interactions among species has always been a basic research focus in ecology. In this paper, we rigorously prove two facts about mutualistic ecological networks based on the Lotka–Volterra model of *n*-species. First, we prove that the dominant eigenvalue of the mutualistic interaction matrix will monotonically increase to infinity as any one of its off-diagonal elements increases to infinity, coinciding with the discoveries by ecologists via simulations. Second, we show that the persistence of mutualistic networks is equivalent to the stability of their interaction matrix. These two results together reveal the fact that the persistence of large mutualistic ecosystems can be guaranteed with proper interaction strengths, though they will eventually be destroyed as the interaction strength between any two species increases.

*Complex Systems* ISSN 0891-2513

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