Chapter 3
METHODS
3.0 Data
3.1 Overview and Goals
The primary goal of this section is to explore different methods in which populations of
urban spaces can be visualized in new ways at various scales. The historical growth of Chicago
has created a landscape in which a system of boundaries exists that is commonly used in
cartographic representations of the city. This boundary system limits the understanding into the
complexity of the urban space and the micro-processes of human settlement in Chicago.
Traditional choropleth and dot density techniques rely on the established boundary units and
represent Chicago’s population in a simplified and typically uninformative way. With
experimentation in the methodological approach to the problem of urban population distribution,
maps and visualizations can be made to better characterize the phenomenon of people in space.
The following methods are investigated in the remainder of this chapter to construct different
visualizations from the available data:
1.
Section 3.2 will explore the vertical residential environment of Chicago and
create a new measurement to describe the living spaces of Chicago- the
measurement of personal space.
2. Section 3.3 will look at the rationale for and the methodological of comparing
demographic profiles as a measure to better understand the significance of the
personal space measurement.
3. Section 3.4 will consider different exploratory spatial statistic models to describe
the geographic distribution of different classifications of living space across the
city of Chicago.
4. Section 3.5 will construct a method to visualize the individual person in the
landscape of the urban environment.
5. Section 3.6 will investigate an alternative approach to visualize the intensity of
people and spaces without the use of traditional boundary units.
3.2 Personal Space Model
3.2.1 Vertical Space Problem
The origin for the following methods is derived from the second research question of this
thesis- in what ways does the vertical extent of neighborhoods obscure our understanding of
spaciousness and crowdedness for urban residents. Chicago is considered the to be the birthplace
of the skyscraper and boast the tallest building in the United States, the Willis Tower- a 110
story, 1454 foot structure in the Loop (Fountain, 2001). The history of skyscrapers in the
redevelopment of post fire Chicago began in 1885 with the completion of the Home Insurance
Building, the first steel-framed skyscraper in the world. Originally constructed with a height of
138 feet, the building was later expanded to a height of 180 feet before being demolished in
1931. Historically, Chicago has played a prominent role in the development of the skyscraper
and at various times in the history of skyscraper development has boasted the world’s tallest
building (Daniel & Grant, 2005).
Louis Sullivan, an urban designer and architect in Chicago recognized that the skyscraper
would represent a new form of architecture in the post fire landscape of Chicago (Kaufman,
1969). Sullivan discarded conventions and designed buildings that emphasized their vertical
nature before adequate technology existed to construct the design. Materials and technologies
were invented in order to realize the Sullivan vision for the new urban space. This new form of
architecture, with an emphasis on the vertical space, became known as the Chicago School of
Design (Kaufman, 1969).
Through the 20th century, Chicago went through two distinct phases of highrise construction- a first boom, from the early 1920s to the mid-1930s, and a second boom from
the early 1960s until the present. The spatial distribution of the high rise buildings are mostly
concentrated in the Loop and along the Magnificent Mile in Chicago's Near North
Side community area (Kaufman, 1969). There are 2,265 high-rises (over 150 feet) structures in
the city of Chicago and 903, about 40%, are zoned for residential use.
With the amount of vertical residential space in Chicago available, the traditional
representations of spaciousness and crowdedness within the boundary units of community area
or census block as characterized by population density are inadequate measurements. The
measurement of population density will not account for the vertical structure of modern urban
residential patterns and could confuse places of high density and places of crowded living
conditions. The aim of this method is to create a new measurement which can account for the
vertical spaces within buildings and reconstruct the idea of population density into one of
personal space.
3.2.2 Model of Vertical Space
The first step in the personal space model is a binary dasymetric approach is used to
separate residential and non-residential structures throughout the city. This method will take the
building footprints for every building in Chicago and eliminates the non-residential structures
based on urban zoning codes attached to each building. The binary approach in this context
deems single-family and multi-family residential structures as suitable for living and places of
business, industry, and other buildings as unsuitable, filtering or masking out the areas deemed
unsuitable (Maantay et al., 2007). A complication with this approach is mix use buildings where
commercial and residential reside in the same structure. Structures such as these are common in
the recently gentrified areas of the city, along major artillery roads, and along natural features
such as parks and waterfronts (Grant, 2002).
Mixed-use development is the zoning of a building or a set of buildings to have more
than more than a singular purpose- not solely residential or commercial space- rather a mixture
of many uses. Mix use developments are created to spatially cluster employment, housing,
commercial, and recreational activities together in a centralized urban space (Duaney, 2002).
Mix use buildings and New Urbanism communities are developed to help eliminate some of the
strain on the local transportation network. A collection of similar mixed buildings, or a New
Urban District, is preferably spatially close to a public transit node (Grant, 2002). Mix use
buildings are often the result of gentrified post industrial urban areas or as part of a planned town
center. In specific zoning terms, mix use development refers to some combination of residential,
industrial, office, commercial, and institutional land uses (Duaney, 2002). In the mix use
building pictured below, small-scale commercial uses fill the street level and residential the
upper two floors. This type of structure is common in the redeveloped spaces of Chicago and
adds a level of uncertainty to the personal space model.
Figure 10-Mix Use Building, Lincoln Park Chicago
This binary dasymetric approach will begin to counteract the generalizations and
arbitrary boundaries of neighborhoods and census zones by assigning only specific buildings as
suitable for living. Mix use buildings, in this step, are considered as suitable for inhabitance by
residents. Later in the model mix use buildings will be divided so that 40% of the space will be
assigned to non residential and 60% to residential. A limitation of the binary approach is that it
assumes homogenous residential space in the buildings distributed across Chicago, and the
model will assign a singular value to the space. This method will only deem a building as
suitable to be included in the residential density formula, and does not account for variation
within buildings. This variable, whether the building is suitable or unsuitable for residential, is
named residential buildings.
Following this, an areal interpolation approach is used to allow for the transformation of
a source data set into a target data set (Mennis 2003). This method is used to aggregate
population values from the different zones to the target layers. In this case, the target layer is the
summation of residential floor space within the lowest level of census measurement, the census
block. This method takes the data within the specified zones from the source data- population
data summarized- and aggregates this into the appropriate zones of the target data set.
Specifically, this method will assign the population of each census block into the buildings
deemed residential in the binary method. The summation of the livable area for each building is
calculated with the product of the residential buildings classification, the area of the building
footprint, and the number of stories for that building. A total livable space is calculated for each
building, represented with a variable livable space. In the case of mix use buildings, 40% of the
livable space will be assigned to non residential and 60% to residential, following the model
used in development simulation experiments (Waddell, 2003). The population of the census
block is assigned to the building based on what percentage of the cumulative livable space
within the census block is the livable space of that building. For example, if one building
accounted for 25% of the cumulative livable space of a census block, 25% of that blocks raw
population numbers would be allocated to that specific building. Areal weighting is a simple
interpolation method which will allocate the summarized population data according to the
proportional area of the zones in the target data (Langford, 2003).
(𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑡𝑖𝑎𝑙 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔𝑠 ∗ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡 ∗ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑟𝑖𝑒𝑠)
𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙 𝑆𝑝𝑎𝑐𝑒 = ∑
𝑐𝑒𝑛𝑠𝑢𝑠 𝑏𝑙𝑜𝑐𝑘 𝑝𝑜𝑝𝑢𝑙𝑎𝑖𝑡𝑜𝑛
Each person within the block will be allocated a percentage of the total residential floor
space within the boundary of the population data. The areal interpolation will again rely on the
assumption that population is distributed uniformly within the target zones (Maantay, 2007), that
the residential patterns within the building are homogenous. Obviously this is not true, but the
level of measurement is constrained by the census data- in other words, the lowest level of
census information, the census block, controls the scale of the project. The buildings can be
mapped as a percentage of the total but individual building variation within the block cannot be
achieved with this approach.
This research is concerned with creating the most accurate and precise representation the
population of the urban environment possible with census data- a detailed illustration of where
and how people live. While having the before mentioned limitations, the use of a dasymetric
technique will expose the limitations of the cartographic technique of choropleth mapping and
the conceptual limitations of urban population density mapping. Moving beyond population
density in the traditional sense, the amount of residential living square footage allotted to each
person is calculated with this – a measurement that can be described as personal space. The
personal space measurement will show not how many people live in an area, but how people live
within that area, how populations are distributed across the built environment of the modern
urban space. A bivariate choropleth design will allow for the spaces in the city where density and
crowdedness are confused to be illustrated.
3.2.3 Bivariate Legend
The bivariate legend allows for spatial comparisons and for the emergence of spatial
patterns in the differences between the traditional population density measurement and the
personal space measurement at the city scale. Using a bivariate map illustrates the correlation
between the traditional measurement and the new measurement, revealing areas of Chicago that
are misrepresented by the traditional population density measurement. This legend is created by
plotting the population density of every census block aggregated to every building within that
census block on the x-axis and dividing that range into three quantiles. This will give each of the
three classifications the same number of observations, essentially creating a high population
density, medium population density, and low population density classification. The range of
personal space is plotted on the y-axis and also divided into three quantiles. This creates a high
personal space, medium personal space, and low personal space classification. The two
classifications are combined together on a three by three grid and symbolized using diverging
color schemes. The diverging color scheme in the bivariate legend of personal space and
population density is applied to every building in Chicago and begin to illustrate where there is
an interesting interaction between the two measurements.
The critical areas of this legend are the four corners- the green, purple, orange, and pink
classifications. The green classification symbolizes places that have a high density and a high
amount of personal space. A high population density suggests that there are many people living
on the planar surface within the boundary unit of the census block. High personal space would
suggest that the people living within this boundary unit are living in residential spaces that are
above average in terms of amount of space per person. The green classification of buildings
suggests that the traditional measurement of population density is insufficient in characterizing
the lived experience of crowdedness or spaciousness in the living space of the built environment.
Likewise, the pink classification illustrates buildings in low population density blocks where the
amount of personal space is below average. Again, this classification illustrates a space where
the traditional measurement has failed to characterize the experience of crowdedness or
spaciousness in the living space of the built environment. The purple classification shows areas
where the population density is high and personal space is low. The orange classifications show
areas where population density is low and personal space is high. The muted colors that form the
cross in the middle signify the spaces in the city that are average in population density or
personal space.
The design of the bivariate legend is done so to illustrate the spaces where the traditional
measurement of population density either adequately captures or fails to characterize the living
spaces of Chicago in terms of the experience of crowdedness or spaciousness of personal
residential space. The personal space metric and population density of the surrounding census
block can be measured in each building in the city. Moving from the building level to the scale
of the entire city, the representation of the bivariate space metric at each building becomes
obsolete. Rather, the most appropriate measure is to summarize the average amount of personal
space per census block and, combined with the census block population density, display the
bivariate choropleth map for the extent of Chicago. This method will essentially break down the
census data to allocate the amount of residential space per person and then reconstructs it at the
census block level for representation. The bivariate metric can be utilized all the way out to the
community area level for a very broad overview of the spatial structure of this interaction. The
allocation of this data to the community level, however, will rely on the boundaries that the
measure itself is attempting to deconstruct and ultimately provides little insight.
3.3 Demographic Profiles of Chicago
A primary purpose of the personal space measurement to is to evaluate the residential
spaces in Chicago and gain a better understanding of how people are distributed across different
spatial environments. In order to better understand this distinction and to explore the implications
of the new measure, this section will examine how demographic distributions change when the
definition of the space is changed. Demographic profiles of neighborhoods or classifications of
neighborhoods are commonly used measures to evaluate the social environment of a space. The
evaluation of the members of a contained micro-environment, such as a bounded neighborhood,
allows for the conceptualization of the socio-economic influences and the socio-cultural features
of a space (Wen et al, 2003). The use of census data to show that a certain percentage of a space
is of one group and another percentage, a different group, is an essential element of the
organizational framework of population analysis. This section will explore this concept and show
the differences in racial classifications when the measurement population density is changed to
personal space
“Obtaining racial data would seem to be a straightforward process: the census asks a
question; statisticians, demographers, and other properly trained professionals tabulate the
responses (Nobles, 2000).
This process however is not as basic as it would initially appear. In the Census form,
respondents are given the choice to select multiple racial categories from the following list of
options: ‘White’, ‘Black or African American’, ‘American Indian or Alaska Native’, ‘Asian’,
‘Native Hawaiian or Other Pacific Islander’, and ‘Other’ (US Census Bureau, 2011). The Census
forms list two ethnicities, ‘Hispanic or Latino’ and ‘Non-Hispanic or Latino.’ The Census
Bureau defines ‘Hispanic or Latino’ as "a person of Cuban, Mexican, Puerto Rican, South or
Central American or other Spanish culture or origin regardless of race” (US Census Bureau,
2011). For this research, I have divided the racial or ethnic self identification into five categories
for analysis and representation: White, Black, Hispanic, Asian, and Other.
To illustrate the differences in the changes in demographics as the value of personal
space is changed; the comparison of high density spaces will be made with the high density, high
space classification- green- and the high density, low space classification- purple. Similarly, the
low density spaces will be contrasted with the low density, high space areas- the orange
classification- and the low density, low space areas- pink. The comparison of the different spaces
will show both percent of total population for the different classifications as well as raw
population numbers. The demographic profiles are collected from the census block
measurement.
3.4 Spatial Structure of Chicago
3.4.1 Spatial Statistics Goals and Overview
The goal of this section is to employ spatial statistic tools and concepts in an exploratory
manner to investigate the distribution of different classified census blocks on the bivariate map
of Chicago. This section is exploratory in nature in that, rather than using spatial statistics to
make concrete or absolute claims about the urban space and the people that inhabit them, the
techniques are being used a tool to begin to understand how different classified areas operate in
space and where would be the most apt place to focus qualitative and quantitative analysis will
be in the future.
The dataset for this section is a point pattern dataset from the city of Chicago that has
16,885 point features representing the centroids of each census block in the city of Chicago. The
points are classified into nine classes based on a bivariate legend explained above- traditional
population density measurement on the ‘y’ axis and personal space measurement on the ‘x’ axis.
The main areas of interest in the analysis are the points that are classified in the four
corners of the legend, the areas that represent the combinations of highs and lows in the
classification- in this case the green, pink, purple, and orange classifications. The green
represents areas of high population density and high amounts of personal space. The purple is
low population density and high personal space. The orange classification is high density, low
space and the pink low in both categories. The 16,885 point dataset for the entire city of Chicago
required sampling for the nearest neighbor analysis. Nearest neighbor analysis works well up to
3,000 points; beyond 3,000 the measurement starts to break down and does not return consistent
variables (Bailey & Gartrell, 1995).
3.4.2 CSR Model
The first test will be testing whether each of the four corners of the bivariate
classification, the four areas of interest, differ in their distribution across the city space from
complete spatial randomness. This will indicate whether the spaces of interest from the bivariate
model show a pattern of clustering beyond what would be expected from a random point pattern.
The first step in this process is to calculate the nearest neighbor calculation on each of the four
areas of interest. The null hypothesis for this experiment is that the spatial distribution of the
classified census blocks is not clustered and is completely spatially random in location within the
city boundary of Chicago. The next step is to simulate a completely spatially random dataset of
3000 points within the city of Chicago with n=39 simulations and calculate the nearest neighbor
of each simulated point for each simulation. This is done to create a distribution of nearest
neighbor results equaling a 95% confidence intervals (Bailey & Gartrell, 1995). This allows for
a distribution for what a complete spatially random pattern would look like which can be
compared to the each classification in an fhat-h plot. This will allow for the comparison of the
different classified point patterns to determine if they are spatially not randomly across the space
of Chicago.
3.4.3 Thomas Model
After determining whether or not the dataset is completely spatially random, the next
logical step is to formally test whether the four point patterns compare to a cluster model. Using
the Thomas cluster model, this test will determine if certain areas of interest are significantly
more clustered than the background population of Chicago census blocks. The purpose of this
experiment is to determine if any of the point patterns are significantly more clustered than a
fairly strong simulated cluster model using a Thomas cluster model with the size and intensity of
the cluster based on a sampling of all the blocks in the city. This approach this will illustrate the
areas that are especially clustered while at the same time taking into account that the point
pattern is derived from census blocks and an artifact of the census structure will be a gridded
pattern. The null hypothesis is that there will be no clustering above what is expected from the
background distribution of census blocks. By using the Thomas cluster model with a radius and
intensity of cluster simulations based on the structure and natural clustering of census blocks, the
gridded structure of the city can be accounted for and classifications that exceed expected
clustering can be observed. The first step is to simulate a Thomas model dataset of 3000 points
within the city of Chicago with n=39 simulations and calculate the nearest neighbor of each
simulated point for each simulation. The intensity of the cluster is calculated using the rate of
clustering from all the census blocks in a community area. This represents the natural clustering
of the city’s census block structure. The radius of the cluster is average length of a community
area centroid to its boundary. The cluster model with the intensity and radius of the cluster set at
this level is designed to replicate the underlying population of census blocks in Chicago. The
model creates 39 simulations to create a distribution of nearest neighbor results at 95%
confidence intervals.
3.4.4 Interaction Model
The next test is an interaction model on all the area of interest point patterns against the
other area of interest point patterns to determine if certain classifications attract or repeal other
classifications. This analysis is performed multi-directionally to determine if one point pattern
holds more weight in the repulsion or attraction interaction. This test will be performed
specifically on the green, pink, purple, and orange classifications against each other in both
directions. Not all of the sets of points have the same number of observations. The following list
shows the number of points each classification has: Green-1,238, Pink- 1,211, Orange- 2,826,
and Purple-2,853. To alleviate any problems that may arise from different size samples, each
classification has been randomly sampled to equal 1,211 observations. The interactions of point
patterns will explain whether one event, the green classification for example, has a direct impact
on the spatial structure a second event, the purple classification for instance. Both events occur in
the same space, the city boundary area of Chicago, but it is unclear whether or not there is an
association between the two.
The null hypothesis is that all couplets of events will be independent of each other and
not show significant signs of attraction or repulsion. For this test, there are two variables, event I
and event J. The interaction method will test to see if the probability that the distance from a
randomly selected object in event I is closer to which of the two point patterns. This is repeated
for every point in the target event. For example, if testing the interaction of the green
classification to the purple classification, each point in green is selected and a nearest neighbor
analysis run to determine if the nearest point is of the green or the purple classification. This will
determine whether the spatial distribution of the purple classification has a direct influence on
the spatial distribution of the green classification.
With the use of exploratory data analysis- the complete spatial randomness model, the
Thomas cluster model, and the interaction model- the spatial structure of how the different
classifications are distributed across Chicago can begin the be explored. Exploratory spatial
statistics are a starting point for beginning to think about what types of social and historical
processes in Chicago are driving the spatial interaction of different lived experiences in different
built environments.
3.5 Dot Density Methods
There are four main considerations when making a dot density map that must be
considered in order to intelligently design the map with implying a misleading spatial
distribution of the phenomena. One must consider the aggregated boundary units, the size of the
dots, the observations per dot, and the location of the dots (Slocum et al, 2009). To understand as
precisely as possible the residential patterns in the urban space, these considerations need to be
narrowed in scope as much as possible. Dots should be placed in the smallest areal unit, the
residential building, to increase the precession of the placement of the individual. Each dot
should represent one person to increase the accuracy of the representation of the individual. To
observe the most accurate map of how people occupy the urban space, the boundaries need to
removed and the individuals represented in space alone.
When making a dot density map, the smaller the polygon the dots are randomly placed
within the more accurate their location will be to the location of the entity being mapped
(Slocum et al, 2009). Ancillary information, in this case, the buildings zoned residential and the
vertical extent of those buildings are used to as the target layer which dots will be placed in. The
population of each individual building is determined by using a Poisson distribution based on the
expected population of each building. The expected population for each building is derived by
calculating the expected amount of space per person from the total population of the census
block into the amount of cumulative personal space measured in the census block. The personal
space measurement will create a measurement that quantifies the amount of residential space in
each building per person, the inverse of that will be the amount of expected people per building.
From the expected intensity, the Poisson distribution allocates individuals into the building to be
represented in a dot density map. This is done under the assumption that all buildings in the
census block are not homogenous both in terms of numbers and in terms of racial breakdown.
The Poisson method, in this case, will account for variation within the buildings and not give
every building in the census block individuals based on the common value of average personal
space.
The dot density method for this series of maps will represent each individual in the city
with a singular dot confined to the building the Poisson distribution estimates that individual to
live. The dots will use a symbology in which the hue of the dot will represent one of the five
census race categories- White, Black, Hispanic, Asian, or Other. The use of chorodots will allow
for the representation of different attributes while maintaining similar size and spatial locations
across all observations (MacEachren, 1990). The chorodot technique will allow for the
representation of different groups of individual people filling the space, both the planar and the
vertical spaces, of the built environment around them. The infrastructure of the urban space
provides a spatial structure of individual residential behavior that operates not on the boundaries
of neighborhoods or census blocks, but rather on the functionality of the residential environment.
The representation of this phenomenon, individuals of different races confined to the buildings
the model predicts them to live in will provide valuable insight into the settlement patterns across
Chicago.
3.6 Intensity Methods
The final methods are designed to use the distribution of people allocated to specific
buildings to create two new maps that show the intensity of people and the intensity of space
without the use of any administrative boundaries. Both maps are made with a kernel density
function to create, first a representation of the population of Chicago with the boundary units
removed, and second, a representation of the degree of crowdedness in Chicago. This map is
designed to model these two population features without relying on boundaries or arbitrary
geographies to determine the areas of classification.
The population intensity map shows the distribution of people across the planar surface
of the city. While this method does not account for the vertical space of buildings, it does use the
personal space measurement as a derivative to create the estimation of how many people live in
each building. The kernel intensity method is designed so that the estimated population value for
each residential structure in the city is accounted for. The kernel radius is a function of that
intensity of the population in each building. The assumption behind this is that the more people
in each building, the more communal space they will occupy and draw resources from when
outside the residential structure. The kernel size function is designed so the population of the
building does not have a huge impact of the kernel size, but does alter it slightly to account for
this allocation of communal space- an indication of the perceived experience of crowdedness of
the space surrounding residential structure. The kernel size is designed so that a single family
home with few residents will have an impact of intensity to match that of roughly a size of a yard
while the most populated structure in the city will have a kernel size of about half a city block.
By having the size of the kernel as a function of building population, the population of each
residential structure will have an impact on the micro-scale population intensity in the immediate
area around the building, but the intensity of the total building population will be the driving
force behind the population intensity map. This map shows the areas of high and low intensity of
populations without the use of any administrative boundaries, but fails to account for the amount
of space each person has. This map is represented using a traditional heat map index with colors
ranging from blue for low intensity to red for high intensity.
The second map, the space intensity map, also employs a kernel density method with a
constant kernel size of 100 feet in diameter. The range of personal space is normalized on a scale
of 0-1 so that the density function will show the distribution of the personal spaces and not the
larger numbers of square feet per person. This method is designed not to calculate the intensity
of the number of people each building has, but to calculate the intensity of the space each person
has. The space intensity map is representing the relative crowdedness or spaciousness of each
building in the city without relying on administrative boundary enumerations. This map is
represented using a heat map index with colors ranging from blue for low intensity of
crowdedness to red for high intensity of crowdedness.
Both the population intensity map and the space intensity map are exported into the
Google Earth interface for seamless viewing and interactivity at multiple scales. By using the
format of an interactive virtual globe, it is immediately noticeable how the intensity of
population and space change based on the built environment and vertical dimension of buildings.
Another useful feature of the Google Earth interactive display is the addition of a three
dimensional model to show the vertical extent of the built environment. In a map of population
or crowdedness with boundaries, the spaces that are non-residential would have the same value
as those places where people live. There is no population that lives on a golf course. A park is
not a spacious or crowded living space. Using this method shows a clear difference in how the
spatial structure of the city changes the intensity of people and spaces without generalizations
and the use of boundaries.
3.7 Summary
The methods section of this thesis employs a variety of techniques in attempts to better
describe and represent the phenomenon of modern urban residential life. The main focus with
this method is working towards the deconstruction of the employment of boundaries in
cartographic representations of urban space. The vertical space is a feature of urban residential
structure that has not been accounted for with the traditional measurements of density and the
representations of density with standard choropleth and dot density approaches. The personal
space index and the bivariate legend are methods to model this vertical space as an active
residential environment. The exploratory spatial statistic models are attempts to discover patterns
across the space of Chicago of the personal space classifications. A fine scale dot density
approach to allocate individuals and demographic characteristics of the individuals to the
building level at a level of representation where each dot equals one person was performed to
explore the microstructure of the built environment in Chicago. A kernel density approach was
taken to represent the intensity of population and the intensity of crowdedness at various scales
across the city without the use of boundaries. The maps created with the methods illustrated in
this section have been placed in the virtual globe environment of Google Earth for seamless user
interaction. The virtual globe environment allows for results to be observed at various scales set
against the context of areal imagery of the city.