b'MUDD 25 - Urban Intensity l Urban Design - Sydneyemployment is likely to remain strong for an extendedtaken together these differing thresholds will display a period.Viewed in this way, urban intensification willmore continuous path over time, thus reinforcing the almost certainly continue and urban design will beexponential decline in the density function.Focusing on affected less by the degree of population density andthe balance over time between the minimisation of travel more by the way intensity works through the experiencestime and the avoidance of over-crowding allows for the of the population that participates in the public realmpossibility of shifting employment to the suburban areas, of an area or neighbourhood.The economic and socialthus instituting a second phase for exponential decay in wellbeing of the relevant population comprise importantnewly formed high-density urban areas. aspects of these experiences.This is examined below in two parts, the first of which focuses on urban densityThis analytical procedure of breaking a complex process and the second on the broader aspect of urban vitality. into smaller parts to gain an understanding of it by searching for answers to the question, why this or why If Urban Intensity is Mainly Urban Density that, forms a major part of social science and goes well beyond a search for numbers in the form of averages or The decline in population density, in proceeding from theestimated coefficients.The test as to how far to proceed city centre to the outer suburbs, was explored duringgenerally emerges with the point at which little or no the second half of the 20th century (Clark 1951, Casettiuseful information is added.For example, Guan & Rowe 1967).Accordingly, let x be distance in kilometres from(2016) developed a methodology for obtaining numerical the centre of the city and let Y be the density of residentestimates for urban (1) compactness, (2) diversity, (3) population in thousands per hectare.Thendensity and (4) connectedness.The first of these used Morans coefficient of spatial correlation, I(Moran 1950):Y = Ce-bxwhere the coefficient C is a measure of the degree of over-crowding that the population is willing to tolerate at the centre of the city and b is the rate of decline ofwhere N is the number of spatial units indexed by i and j, density, for which a low value would indicate a slowx is the population in the sub-areas, xij, withdenoting decline as distance increases.Of special interest tothe arithmetic mean of all units, Wij is the matrix of urban planners and designers is the way in which theweights with the diagonal elements, xii, set equal to zero density gradient changes over time.It will flatten outand W is the sum of all weights.Similarities between if the suburbs absorb a greater share of the populationunits are calculated as the product of the weighted increases and will fall more steeply if the city centredifferences between the distances, xi (and xj) with becomes regenerated (Broitman 2019). the overall mean, and when divided by the variance it produces a measure of correlation between the spatial Perhaps of greater importance than the numericalunits in reference to their respective populations.A values for the components of the density functionvalue of minus 1 would indicate a perfect clustering of are the reasons to expect changes in their respectivedissimilar populations, while a value of plus 1 would values.The explanation in this case begins with thebe associated with a perfect clustering of similar supposition of two choices for households to locate atpopulations.Consequently, this measure is somewhat some distance from the centre.First is the minimisationmore elaborate than the previously described measure of time and expense of travelling from the place ofof urban density, and would indeed by a better measure residence to the place of work which, at least in theof actual compactness within the boundaries of i and beginning, is presumed to be near the city centre. j.As noted previously however, it is the threshold or The second is the preference for non-congested sitestipping point for over-crowding that may be the principal for residence as expressed in the form of a disutilitydeterminant for a change, so it is not obvious that conveyed by C in the equation above.For individualelaboration is either desirable or practical. households this may be viewed as a threshold beyond which the desire to seek greater distances from the cityA method of measuring diversity is referred to as the centre becomes apparent.However, for all householdsShannon index of entropy, or the phylogenetic index.20P1-20200229-FOLIO INTRO.indd 23 2020/3/6 22:10:45'