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Development Process
Step 1: Identify the components and define the variables.
Step 1: Identify the components and define the variables.
The first step in developing an algorithm is identifying the components of the subject you are analyzing. In the case of Scottsdale, we needed to identify all the components that take up land within the city. These things include roads, natural topography like mountains and rivers, businesses, warehouses, farmland, houses, apartments, condos, townhouses, resorts, and universities. Rather than account for every object in the city, which will take more time than we have available, we will put these things into categories. For the sake of simplicity, we will put houses, apartments, condos, and townhouses into one category and we will put everything else into a single category that accounts for everything that is not a housing unit.
We can give this information an equation that looks like this:
Scottsdale Total Area sq miles = (# of Housing Units) sq miles + (# of Everything else) sq miles
Step 2: Identify a recognizable and manageable pattern to aid in calculations.
Step 2: Identify a recognizable and manageable pattern to aid in calculations.
Fig. 3: Screenshot of Scottsdale map with gridlines overlaid
While observing the maps of Scottsdale, we noticed that the city is organized into various grid-like configurations. In the image above, there are 2 identical squares. These are the smallest standard-size grids and all other configurations are made up of any number of these smaller grids. Larger grids are then made up of previously configured grids. The presence of a consistent pattern allowed us to shrink the workload by being able to take the average contents of a series of grids and use that information in our calculations. This grid pattern also allowed us to further develop the equation mentioned in step 1. In step one, we identified that the total area of Scottsdale is made up of the total area of housing units plus the total area of everything else. Since the city is made up of grids, we can replace the area unit with grids.
Total Area = Total # of Grids X Area of one Grid
Total # of Grids = % of grids that have houses + % of grids that have no houses
Step 3: Develop the equation further and add details to increase the accuracy of the estimation.
Step 3: Develop the equation further and add details to increase the accuracy of the estimation.
Using a zoning map from the City of Scottsdale's website, we were able to identify the different zones that lie within the city. This resource would allow us to make estimations for the concentration of the residential areas in Scottsdale. This resource also allowed us to define different types of grids that contain houses. Within the Zoning map, we were able to identify 4 types of grids that contain houses. These include Rural, Suburban, Urban, and Mixed-Use Neighborhoods. With this distinction, our equation evolves just a little bit. The Equation is as follows:
Total # of Grids = % of Rural Grids + % of Suburban Grids + % of Urban Grids + % of Mixed-Use Grids + % of all other Grids
Fig. 4: Screenshot of Scottsdale zoning map legend
Step 4: Determine the average number of buildings in a standard grid.
Step 4: Determine the average number of buildings in a standard grid.
After we determine the concentration of each type of neighborhood within Scottsdale, we need to determine the number of housing units that are contained within each grid. To do this, we will select a sample size of 3 grids for each type of grid. We will manually count the number of housing units per grid and then take the average across those three grids. Below are examples of the sample grids we used for our calculations. Once we have identified the average number of housing units for each type of grid, we can multiply the number of grids of that type by the average number of housing units for that type of grid. The equation will look something like this:
Total # of Housing units (Rural) = # of grids (Rural) * # of housing units per grid (Rural)
Where,
# of housing units per grid = (Sample 1 + Sample 2 + Sample 3) / 3
This Equation can be repeated for every type of grid that contains housing Units.
Rural
Rural
Fig. 5: Rural sample grid
Suburban
Suburban
Fig. 6: Suburban sample grid
Urban
Urban
Fig. 7: Urban sample grid
Mixed-Use
Mixed-Use
Fig. 8: Mixed-use sample grid
Step 5: Calculate the total number of housing units
Step 5: Calculate the total number of housing units
To do this, all we would need to do is take the number of grids for each type of grid and multiply them by the number of housing units in one grid of that type. Then we would only need to add up all the houses in a type of grid to get the total number of houses in Scottsdale. As a recap our Equation progression is as follows:
Step 1: Identify the Components needed for the calculation.
Total Area = Area of houses + Area of everything else
Step 2: Convert Area Units into more manageable units. In this case, we are using grids.
Total number of Grids = Total Area / Grid Area
Total number of grids = number of grids with houses + number of grids without houses
Step 3: Identify the types of grids that contain houses. Substitute them into the equation.
Total number of grids = number of rural grids + number of suburban grids + number of urban grids + number of mixed-use grids + all other grids
Step 4: Determine the values of concentration for each type of grid.
Total Area = %Rural +%Suburban + %Urban +%Mixed-use +%Everything else
Substitute grids back into the equation
Total number of grids = %Rural grids +%Suburban grids +%Urban grids +%Mixed-use grids +%All other grids
Step 5: Determine the number of housing units per grid.
Number of Rural houses per grid = (Sample 1 + Sample 2 + Sample 3) / 3
Number of Suburban houses per grid = (Sample 1 + Sample 2 + Sample 3) / 3
Number of Urban house per grid = (Sample 1 + Sample 2 + Sample 3) / 3
Number of Mixed-use houses per grid = (Sample 1 + Sample 2 + Sample 3) / 3
Step 6: Determine the amount of each type of grid.
Number of Rural grids = Total number of grids * %Rural grids
Number of Suburban grids = Total number of grids * %Suburban grids
Number of Urban grids = Total number of grids * %Urban grids
Number of Mixed-use grids = Total number of grids * %Mixed-use grids
Step 7: Calculate the total number of houses for each type.
Number of Rural houses = Number of Rural grids * number of Rural houses per grid
Number of Suburban houses = Number of Suburban grids * number of Suburban houses per grid
Number of Urban houses = Number of Urban grids * number of Urban houses per grid
Number of Mixed-use houses = Number of Mixed-use grids * number of Mixed-use houses per grid
Step 8: Calculate the total number of houses in Scottsdale.
Total number of houses = Number of Rural houses + Number of Suburban houses + Number of Urban houses + Number of Mixed-use houses
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