1. A Python-based Algorithm for Enhanced Dot
Density Thematic Mapping
Daryn Hardwick
Saint Cloud State University
Department of Geography & Planning

2.  The Problem
 Expectations/Hypothesis
 Background
• Python
• Center of Gravity Principle
• Improvements to the Dot Density Technique
• Anonymity in Agricultural Data
 Methods
• Algorithm
• Test on Agricultural Data
 Results
 Additional Functionality
 Discussion/Conclusion
• Critiques of the Algorithm
• Future Research

3.  Randomness in Dot Density Thematic
Mapping
• Use of GIS Software
 Tobler’s First Law of Geography
• “…near things are more related than distant things”
 Previous Solutions
• Drawing Programs
• Feature masks

4.  Expectation
• The algorithm presents a solution to the problem of
randomness using the center of gravity principle
 Hypothesis
• The dots produced from the algorithm will be
significantly closer to actual farmland than the
random dot distribution produced by GIS software

5.  What is Python?
• An object-orientated scripting language
 How does it work?
• Methods (procedures) performed on or between
objects1
• In GIS, objects are data with properties
 Why Python?
• ArcGIS compatibility
• Software quality, developer productivity, program
portability, support libraries, component
integration, and enjoyment2
1: (Stefik and Bobrow 1985)
2: (Lutz 2008)

6.  What is the center of gravity principle?
• “…the cartographic ideal, back when all dots were
placed manually, has been to locate the dots as
close to the real distribution as possible.”1
 Algorithm provides solution
• Placement of known points
1: (Dent et al. 2009)

7.  Earliest dot maps 1
• 1852 – cholera maps by August Petermann
• 1863 – Maori population in New Zealand
 Percentage Dot Maps 2
 Limiting amount of dot overlap 3
 The “Fuzzy Dot Map” 4
1: (MacEachren 1979)
2: (Mackay 1953)
3: (Kimerling 2009)
4: (Alqvist 2009)

8.  USC (Title 7, Chapter 55, § 2204g) 1
• “…information obtained may not be used for any
purpose other than statistical purposes for which
the information is supplied.”
 Algorithm does preserve anonymity
1: (Department of Agriculture 2008)

9.  Critical Inputs
• Enumeration unit areas
• Known point locations
• Two Geodatabases
• Areas to be masked from receiving dots (i.e. Water)
• Dot value
 Additional Inputs
• Clustering
• Number of Buffers

10.  Split of enumeration areas
 Area and buffer distances are calculated

11.  Why use variable width buffers?

12.  Split of enumeration areas
 Area and buffer distances are calculated
 Buffers clipped
 Number of output dots calculated
 Buffered areas merged
 Enumeration areas merged
 Areas excluded from output dots masked
 Creation of the output dot map

13.  2007 Census of
Agriculture
• Acreage, number of
farms, market value of
ag. products sold
 Dots created using the
algorithm and random
dot placement tested
 Near analysis
 Significance Testing
Land Cover data retrieved from the
2006 National Land Cover Dataset

14. Market Value
Acreage of Number of Of Agricultural
Farmland Farms Products Sold

15. Random Algorithm
One dot represents
12,800 acres
68.33% On Farmland 70.14%
141.37 meters Distance to 103.39 meters
Farmland

16. Random Algorithm
One dot represents
40 farms
63.01% On Farmland 65.31%
189.01 meters Distance to 125.82 meters
Farmland

17. Random Algorithm
One dot represents
$5,000,000
72.51% On Farmland 76.39%
66.38 meters Distance to 38.82 meters
Farmland

18. T-score P-value Significant?
Acreage: -1.93 0.0269 Yes
Number of farms: -2.72 0.0033 Yes
Market value: -3.74 0.0001 Yes

19.  Operation within
ArcGIS
 Custom Toolbox
 Two Parts
• Step 1 – Script
• Step 2 - Model

20. Algorithm run with a low clustering effect Algorithm run with a high clustering effect

21. Algorithm run with a two buffers Algorithm run with a four buffers

22.  Critiques
• Time
• Placement of Known Points
 Future Research
• Improve the issue of time
• Another way to solve this problem?

23.  This algorithm
• Increases the accuracy of placed dots
• Adheres to the center of gravity principle
• Removes some randomness without sacrificing
anonymity of underlying data
• Can be used in ArcGIS
• Options to further customize the output

24.  Ahlqvist O., (2009) “Visualization of Vague Category Counts – Introducing the Fuzzy Dot
Density Map”. In: International Cartographic Conference 2009 Proceedings, International
Cartographic Association.
 Dent B., Torguson J., and Hodler T., (2009) “The Dot Density Map”. Cartography: Thematic Map
Design, 6e: 119-130.
 Department of Agriculture, (2008) “Authority of Secretary of Agriculture to conduct census of
agriculture”. U.S. Code Title 7, Chapter 55, § 2204g.
 Golledge R., (2002) “The Nature of Geographic Knowledge”. Annals of the Association of
American Geographers, 92(1): 1-14.
 Hey A., (2012) “Automated Dot Mapping: How to Dot the Dot Map”. Cartography and
Geographic Information Science, 39(1): 17-29.
 Hoonaard W., (2003) “Is Anonymity an Artifact in Ethnographic Research?”. Journal of Academic
Ethics, 1: 141-151.
 Kimerling A., (2009) “Dotting the Dot Map, Revisited”. Cartography and Geographic
Information Science, 36(2): 165-182.
 Lutz M., (2008). “A Python Q&A Session”. Learning Python, 3e: 3-20.
 MacEachren A., (1979) “The Evolution of Thematic Cartography / A Research Methodology and
Historical Review”. The Canadian Geographer, 16(1): 17-33.
 Mackay J., (1953) “Percentage Dot Maps”. Economic Geography, 29(3): 263-266.
 Stefik M., and Bobrow D., (1985). “Object-Orientated Programming: Themes and Variations”.
AI Magazine, 6(4): 40-62.
 Tobler W., (1970) “A computer movie simulating urban growth in the Detroit region”.
Economic Geography, 46(2): 234-340.

25. Graduate Student
Saint Cloud State University
daryn.hardwick@yahoo.com