This paper suggests a plausible explanation for the spatial evolution of high-rise buildings. Contrary to intuitive expectations the histograms and spatial distribution in cities indicate peculiar and non-continuous patterns. These patterns evolve as a result of developers' behavior in real-estate markets. One of the critical variables in decision-making of developers is time. Despite obvious differences in land prices within a particular real-estate market, differences in costs and prices are relatively small in comparison to differences in their time incidence. The paper presents a simple search model of land developer that suggests interesting explanation of the spatial sprawl of cities. The central parameter in our model is "characteristic time", the period of time from the acquisition of initial property rights in the land and until the first return on the investment is realized. The model leads to leapfrogging patterns, particularly during downturn periods and explains the appearance of high-rise buildings in the urban periphery. JEL Classification R11 · R12

Contrary to the popular notion that the advancing frontier of urban development has been swallowing and destroying natural ecosystems we present evidence that the sprawl of cities creates ample open space in peri-urban areas. Traditional view of city-nature dichotomy and clear spatial separation should be substituted by a vision that reflects the complex spatial dynamics of city-rural-natural fabric with extended areas of overlap among them. We present a survey of the relevant research concerning urban and ecological systems spatial dynamics and conclude that nonregular, leapfrogging spatial expansion, characteristic of the majority of the modern western cities, may buffer between urban and intensively cultivated agricultural areas and counter their impacts on natural ecosystems. The wealthy sprawling suburbs provide essential habitats for native species and ensure their survival.

This paper presents a quasi-3D cellular automaton (CA) simulation model of cities. A 2D CA model includes a cell attribute that represents building height information. Dynamic processes are depicted using four parameters: initial building coverage, interaction with adjacent neighborhood, inertia, and noise. These parameters can assume simple economic interpretation. Some combinations of values of the parameters result in cities that experience paths of convergent growth. Some values lead to cities that experience phase transitions. We suggest a typology of resulting urban patterns and note the emergence of spatial clusters of high-rise buildings.