# Chapter 3 - Part 2: Thematic Maps

This chapter covers various types of maps and their features. Many types of maps exist so that cartographers can visualize spatial phenomenon in the most advantageous way. It is important that you be aware of all the different map types available to you so that you can visualize your data in the format that will be most appropriate for the content of your map and your map user. This lesson covers three map types: choropleth maps, proportional symbol maps, and dot-density maps. This part of the chapter covers proportional symbol maps, and dot-density maps.

## 3.2: Proportional Symbol Maps

On a proportional symbol map, a symbol’s size is buried in proportion to the quantity it represents. The most common symbol used in a proportional symbol map is a circle. On this example proportional symbol map, it shows the total population per state in the year 2007 for the United States of America. The circles vary in size as the total population it represents increases. On this map, map readers can quickly and easily determine which states have the largest population in relation to other states.

Figure 9: Proportional Symbol Map

Why Create Proportional Symbol Maps? So why should you create a proportional symbol map? A proportional symbol map is easy for map readers to understand. Multiple variables can be displayed simultaneously on a proportional symbol map. For example, the symbol's size, symbols color, and symbols a shape can all represent different variables.

Additionally, you can overlay a proportional symbol onto another type of thematic map such as a choropleth map. Finally, the main reason to create a proportional symbol map is when you want to display a quantitative distribution of a variable throughout space.

Why not Create Proportional Maps? Here is why you should not create a proportional symbol map. In general, map readers tend to underestimate the relative size of the symbols on the map this leads to over or underestimation of values. Also, symbols can easily overlap too much a dense location in the user will not be able to see enough of the symbols to determine the values in the map will look cluttered.

Appropriate Data: Appropriate data for a proportional symbol map is either total values, percentage values, or rate values. Additionally, the data should occur at a point or the data should be aggregated to an enumeration unit such as accounting. If the data is aggregated to a point within an area the dot is typically placed in the center of the area.

Inappropriate Data: Inappropriate data for a proportional symbol map is interval data. As the size of a symbol can be reduced to 0, which is a natural 0 state for the symbol, the data should have a natural 0 point. This would exclude data that does not have a natural 0 point such as temperature. Another type of inappropriate data for proportional symbol map is data with small ranges in the values. Data with small ranges of values will make for an interesting map as the size of the symbols will not vary too greatly. There is also density data. Density data is not appropriate for a proportional symbol map and you should consider making a choropleth map instead.

Projections: The equivalent or equal-area projections are the most appropriate map projections for the proportional symbol map. Since the relative size is important to maintain and comparing values within enumeration units you should choose a map projection that maintains the relative sizes of the areas.

Proportional Symbols: Now consider the proportional symbols themselves. Various shapes can be used for proportional symbols although the circle is the most common. There are two categories of point symbols that we can use: geometric symbols, and pictographic symbols.

A geometric symbol can be either two-dimensional or three-dimensional and it should not look like the image or area that is being mapped.

Two-Dimensional symbols: Examples of 2-D geometric symbols are a circle, a triangle, and a star. A pictographic symbol looks like the thing being mapped. First focus on the two-dimensional geometric symbol as this will probably be the most common symbol you will use of a proportional symbol map. For the 2-D geometric symbol, the area of the symbol is a scale to represent the magnitude difference of the value of represents. The circle is the most widely used symbol of a proportional symbol map.

The advantages of using a circle are that its geometric form is compact and the circles are visually stable since the eye does not wander across the circle too much. If circle symbols overlap they can still be effective in indicating magnitude. And finally, circles can easily, lend to a second variable by changing its color or texture. Squares are also popular choices as their main advantage is that the proportional areas are nearly perfectly perceived whereas they will be over or underestimated for circles and most other two-dimensional geometric symbols.

A disadvantage of using squares is that it adds “squareness” to the map which may not be desirable. It can also be confused for other common symbols like houses.

Figure 10: (left to right) 2-D Circle, Triangle, and Star

Three Dimensional symbols: Three-dimensional geometric symbols can also be used as proportional symbols. Examples of three-dimensional geometric symbols are a sphere, prism, or pyramid. The advantages of three-dimensional geometric symbols are that they are visually attractive and they allow for less crowding of the map because they add the third dimension which allows it to be slightly more compact.

The disadvantages of three-dimensional geometric symbols are that readers cannot accurately judge scaling differences because the readers now have to judge changes in volume. Range grading the symbols is recommended for three-dimensional symbols to combat scaling issues. Complicated three-dimensional geometric symbols can also be hard to understand on a map.

Figure 11: 3-D Square and Cylinder

Pictographic: Pictorial symbols are sometimes good choices for proportional symbols. Advantages of pictorial symbols are they are visually attractive and attention-grabbing. Disadvantages for pictorial symbols are the more regular the shape of the control symbol, the harder will be to perceive the magnitude differences. Additionally mapping a second variable is difficult except for simple hue changes.

Three examples of pictographic symbols are the front of a bus, and outline of an airplane, and a taco.

Figure 12: Pictograms of a Bus, Airplane, and Taco

Proportional Symbol Color: Now consider proportional symbol color. Different colors apparently do not affect the estimation of symbol size differences. Symbols that are too darkly tinted command a lot of attention so you should avoid extremely dark symbols unless you wish them to command a significant amount of attention on the map.

Symbols with little contrast from its surroundings may be lost and are not popular choices. You should consider using appropriate strategies for contrast. Symbols that are black or gray colors are the most popular with map readers for a proportional symbol map. And finally, changing the color of the symbol can be used for a second variable.

Overlap: Sometimes on proportional symbol map symbols will overlap. Overlapping symbols express a sense of visual cohesiveness and may make the map more memorable to the user as it will make a strong visual imprint in their mind. The downside to symbol overlap is that it may make it harder for the map reader to estimate the individual symbol sizes as they will be partially obscured.

To combat this try not to overlap symbols more than 25% to 33%. Additionally, when symbols overlap, smaller symbols must cover the larger symbols as shown in Figure 13. If you cannot avoid significant symbol overlap another option is to make the circles transparent, or semitransparent to help users perceive overlapping symbols.

Figure 13: Overlap

Appropriate Overlap: The maps in Figure 14 are examples of maps, using appropriate symbol overlap. In both maps the symbols overlap state outlines and other proportional symbols but not so significantly that you cannot estimate the size of the circles that are being obscured. Additionally, with this amount of symbols overlap, the map has a cohesive feel to it in a large amount of overlap in the northeast part of the United States makes the data memorable.

Figure 14: Appropriate Overlapping on a Map

Inappropriate Overlap: Figures 15 and 16 are examples of inappropriate amounts of symbol overlap. In Figure 15 there is too little overlap which makes it seem empty and uninteresting. On the map on the right, there is too much overlap of the circles which causes circles to be obscured. Also, the proportional symbol for California exceeds the neat line of the map which looks very messy.

Figure 15: Little Overlap, Empty, Uninteresting
Figure 16: Too Much Overlap

Scaling Methods: There are three primary methods of scaling proportional symbols: absolute, apparent magnitude, which is also known as perceptual, and range grading.

Absolute Scaling: In absolute scaling symbols scale proportionally to their data values and to each other. Absolute scaling is great if you want each symbol to be unique in size and to give a true visualization of the relative values. The negative aspect of absolute scaling is that it can be difficult for the map user to interpret because the map user can only differentiate a given number of symbol sizes effectively.

Figure 17: Absolute Scaling

Apparent Magnitude Scaling: In apparent magnitude scaling it applies factors to compensate for the user's underestimation of area and volume of the symbols. Typically this factor is used to increase the size of the circles faster than in absolute scaling. Apparent magnitude scaling is also known as Flannery, perceptual, or psychological scaling. Looking at the two example legends in Figure 18, there are five proportional circles in each legend, with the same value; however, the circle sizes and the apparent magnitude scaling legend are a bit larger to compensate for the map user’s tendency to underestimate relative areas of the circles.

Figure 18: Comparing Absolute and Apparent Magnitude Scaling

Range Grading Scaling: Another type of scaling is range grading scaling. In range grading scaling each symbol, size represents a range of data values and not a single data value. Range grading is similar to choropleth mapping as you employ data classification methods to determine class breaks. The main advantage to range grading scaling is that readers can easily discriminate symbol sizes and match them to the legend symbols.

For instance, if there are five circles on the legend of different sizes and there will only be circles of five different sizes on the map it should be easy for the map reader to match the symbols from the map to the legend thereby getting the range of values for that location. Range grading is recommended for three-dimensional geometric or pectoral symbols as users tend to have difficulty in estimating sizes properly for the symbols.

Figure 19: Range Grading Scaling

Redundant Coding: One option available to you when creating a proportional symbol map is the idea of redundant coding. Redundant coding is the use of more than one visual variable to differentiate the symbols from each other. For example, as the value of the attribute increases, we can increase the size of the symbol and darken the color of the symbol. By using more than one visual variable to differentiate the symbols, this reinforces the idea of increasing or decreasing magnitude.

The most common way in which redundant coding is used on a proportional symbol map is through varying the lightness and hue in concert with the size of the symbol. In this case, lighter colors should represent lower values and darker colors should represent higher values. If the circles represent one kind of thing, and it is recommended that you choose a single color and simply vary the lightness and darkness.

Figure 20 is an example map that employs redundant coding. The smaller circles are colored with lighter colors and represent smaller values. The higher values used darker colors to represent higher values. Using redundant coding can add a nice visual impact on the map.

Figure 20: Redundant Coding

Reference Features: Now you can consider the use of reference features on a proportional symbol map. Again, thematic maps should be simple by design so that the map user can focus on the proportional symbols and the data they represent. You should avoid placing reference features unless they are important in explaining the pattern of the variable being mapped.

Legend Design: On a proportional symbol map, the legend serves as a visual anchor for interpreting symbol sizes. There are four common legend layouts, which are: vertical, horizontal, nested symbols, and nested semi-symbols. In these different legend layouts numbers or data values are placed to the right of the symbols with the vertical or nested legend layout and below the symbols if it is a horizontal layout.

Vertical Layout: For the vertical legend layout, the values are displayed to the right of the symbol. Also, small values are at the top and large values are at the bottom.

Figure 21: Vertical Layout

Horizontal Layout: For the horizontal legend, layout values are below the symbols and small values are on the left and large values are on the right.

Figure 22: Horizontal Layout

Nested Symbols Layout: In the nested symbols legend layout, the symbols are placed on top of each other with the smallest symbol on top of the largest symbol on the bottom. The symbols are also a line along their tops or bottoms.

The main reason to use a nested symbols legend layout is that it requires less space on the map layout and the vertical or horizontal legend layout. To save even more space you can place the values inside the symbols if there is space available, otherwise, the value should be to the right of the nested symbols with a leader line connecting the values to the symbols.

Figure 23: Nested Symbols Layout

Nested Semi-Symbol Layout: The nested semi-symbols legend layout requires the least amount of space on a map. This is essentially the legend of the nested symbols but with half of the symbol missing and replaced with the values. You may also have leader lines from the top of the symbols to values as well.

Figure 24: Nested Semi-Symbol Layout

Proportional Symbol Map - Legend Design: With respect to legend designed for proportional symbol maps, there are a few special cases to consider. If a single, or if your values are significantly larger or smaller than all the other values, we may consider these outliers. In the case of outliers, we can label the symbol on the map with its name and value to bring attention to it. We can also label the symbol on the legend with each unique name and value or change the color of the outlier to bring attention to it to show that it is different in some way than the other symbols. If there is not much congestion on the map it is okay to label the proportional symbols on the map itself with their values.

## 3.3: Dot Density Maps

A dot density map is a map showing total values represented by randomly placed dots within an enumeration area to represent density and spatial distribution. This example map shows population density for the year 2007 for the United States of America.

On this map, 1 dot represents 200,000 people. Each dot is randomly placed within its enumeration unit, which in this case, is the county. Where the dots are denser on the map the user will interpret this area as having more value. Where there are fewer dots on the map, the user will interpret this are having less value.

Figure 25: Dot Density Map

Why Create a Dot Density Map? A dot density map is easy to create and easy to interpret. It excels at displaying a variable’s overall geographic pattern and density. Counting the number of dots in an area will allow the map user to ascertain total values with some rounding error. Dot density maps can reflect distributions more accurately than other thematic map types.

Why Not Create a Dot Density Map? So why should you not create a dot density map? First, map readers do not perceive dot densities linearly; they may overestimate or underestimate the densities of the dots as density increases in an area. Second, the dots may not be automatically placed close to the phenomenon they represent since the dots are randomly placed.

Third, the large ranges of data values make it hard to choose a single dot value. Fourth it may be hard for the map users to recover original totals when dots are placed close together making it hard to pick out individual dots. Fifth and finally dots may appear where they cannot possibly exist. For example, a dot representing cattle may show up in a lake when that does not make sense for the dot to be there.

Appropriate Data: Total values are the types of data that are appropriate for a dot density map. The data should be represented and aggregated to an enumeration area. You should strive for the smallest enumeration units possible to maximize the likelihood that the dot will be placed close to the location of the phenomenon. Generally, the enumeration units themselves should not be shown on the map.

If you wish to show the enumeration units on the map, either deemphasize enumeration units or keep the enumeration units off the map and shows the next level up of an enumeration unit. For example, if our data’s enumeration unit is counties, then we could not show counties of a map, but instead, show state boundaries. Data sets that do not have large or small ranges are also appropriate for a dot density map. If the data set has a small range of values it will lead to a uniformed look on the map. If the data set has a large range of values it will be hard to choose a good size.

Inappropriate Data: Inappropriate data for a dot density map is continuous data that is not controlled by an enumeration unit. Data sets with small or large ranges are not appropriate. Derived data such as persons per square mile is not appropriate for a dot density map.

Map Projections: The best map projection for a dot density map is the equivalent or equal-area map projection. As the relative size is important to maintain when comparing values within enumeration units, you should choose a map projection that maintains relative size.

About the Dots: It is important that on all dot-density maps each dot represents more than one item. If the dot represents exactly one item then the dot should be placed exactly where the item it represents is located. If this is the case then what you are creating is a general reference map, not a dot density map.

Dots should be large enough to stand out but small enough to not be totally dominant on their own. Generalization of the dot values occurs at one half of the dot value. That means a dot that has the value 100,000 can be considered to represent all values between 50,000 and 149,999. Each dot is a spatial proxy which means that the dots are placed around the center of gravity of the geographic phenomenon.

Random Placement: Each dot is randomly placed inside the enumeration unit. The dots are randomly placed to avoid giving the impression that the dots are precisely placed and to avoid regular placement of the dots having large values. You can use ancillary data to restrict the placement of dots. For example, you could tell the software to not place the dots within lakes if it does not make sense for the dots to appear within the lake.

General Dot Guidelines: Here are some general dot size guidelines. Enumeration units with the smallest value should have about two to three dots inside of it. Dots should just begin to coalesce in the most dense enumeration area. Dot values should be easy to understand and to count with. For example, 500 and 1000 are good dot values.

Good Dot Size and Value: In Figure 26, the dots are of a good size and of good value. In the densest area of the maps, the dots just begin to coalesce; you can still generally pick out each individual dot.

Figure 26: Good Dot Size and Value

Good Dot Size, Poor Value: In Figure 27 the dots are of a good size; however, the dot value was chosen poorly and is too large. Because the dot value is so large most of the map looks sparse and the densest areas do not give a good feeling of high density.

Figure 27: Good Dot Size, Poor Value

Poor Dot Size, Good Value: In Figure 28 the dots are of a poor size but the dot value is good. As the dot size is so small it still leaves the map looking sparse. The dot size should be increased so that the dots are easier to see and the map looks more filled in.

Figure 28: Poor Dot Size, Good Value

Other Symbols: It is possible to use other symbols than dots. You can use geometric shapes which are familiar to map readers and are simple and easily recognizable at multiple sizes. Another option is to use pictorial shapes which may add to the theme and memorability of the map. The negative aspect of pectoral shapes is that if the pectoral shapes are too complex they may not scale well to multiple sizes.

Reference Features: With respect to reference features on a dot density map, like other thematic maps, it too should be kept simple by design. You should avoid placing reference features unless they are important in explaining the pattern of the variable being mapped.

Dot Density Map - Legend Designs: Designing legends for dot density map is fairly straightforward. On the legend you should have a representative symbol and a statement about the value of that symbol. Rarely are legend headings required for a dot density map legend. You can include additional information in the legend if necessary, such as the total of all values of a map, or representation of what a low, medium, and high density looks like on the map.

Figure 29: Legend Design

## Other Resources

Dot Density Maps in ArcGIS Pro

Dot Density Maps in ArcGIS Online

Graduated Symbols in ArcGIS Pro

Proportional Symbols in ArcGIS Pro

## Summary

This chapter covered various types of maps and their features. Choropleth, Dot Density, and Proportional Symbol Maps were exhibited and explained. You learned about appropriate and inappropriate data as well as data classifications and symbolization for each map type. Map legends and the elements that should be considered when using this feature were also covered.

## Credits

This work by the National Information Security and Geospatial Technologies Consortium (NISGTC), and except where otherwise noted, is licensed under the Creative Commons Attribution 3.0 Unported License.

Authoring Organization: Del Mar College

Written by: Richard Smith

Copyright: © National Information Security, Geospatial Technologies Consortium (NISGTC)

Development was funded by the Department of Labor (DOL) Trade Adjustment Assistance Community College and Career Training (TAACCCT) Grant No. TC-22525-11-60-A-48; The National Information Security, Geospatial Technologies Consortium (NISGTC) is an entity of Collin College of Texas, Bellevue College of Washington, Bunker Hill Community College of Massachusetts, Del Mar College of Texas, Moraine Valley Community College of Illinois, Rio Salado College of Arizona, and Salt Lake Community College of Utah.

This workforce solution was funded by a grant awarded by the U.S. Department of Labor's Employment and Training Administration. The solution was created by the grantee and does not necessarily reflect the official position of the U.S. Department of Labor. The Department of Labor makes no guarantees, warranties or assurances of any kind, express or implied, with respect to such information, including any information on linked sites, and including, but not limited to accuracy of the information or its completeness, timeliness, usefulness, adequacy, continued availability or ownership.