Designed by Thomas Gaskin. Creative direction by Hugh Dubberly. Algorithms by Patrick Kessler. Patent belongs to William Drenttel + Jessica Helfand.

This poster illustrates a change in design practice. Computation-based design—that is, the use of algorithms to compute options—is becoming more practical and more common. Design tools are becoming more computation-based; designers are working more closely with programmers; and designers are taking up programming.

Above, you see the 892 unique ways to partition a 3 × 4 grid into unit rectangles. For many years, designers have used grids to unify diverse sets of content in books, magazines, screens, and other environments. The 3 × 4 grid is a common example. Yet even in this simple case, generating all the options has—until now—been almost impossible.

Patch Kessler designed algorithms to generate all the possible variations, identify unique ones, and sort them—not only for 3 × 4 grids but also for any n × m grid. He instantiated the algorithms in a MATLAB program, which output PDFs, which Thomas Gaskin imported into Adobe Illustrator to design the poster.

Rules for generating variations
The rule system that generated the variations in the poster was suggested by Bill Drenttel and Jessica Helfand who noted its relationship to the tatami mat system used in Japanese buildings for 1300 years or more. In 2006, Drenttel and Helfand obtained U.S. Patent 7124360 on this grid system—“Method and system for computer screen layout based on recombinant geometric modular structure”.

The tatami system uses 1 × 2 rectangles. Within a 3 × 4 grid, 1 × 2 rectangles can be arranged in 5 ways. They appear at the end of section 6.

Unit rectangles (1 × 1, 1 × 2, 1 × 3, 1 × 4; 2 × 2, 2 × 3, 2 × 4; 3 × 3, 3 × 4) can be arranged in a 3 × 4 grid in 3,164 ways. Many are almost the same—mirrored or rotated versions of the same configuration. The poster includes only unique variations—one version from each mirror or rotation group. Colors indicate the type and number of related non-unique variations. The variations shown in black have 3 related versions; blue, green, and orange have 1 related version; and magenta variations are unique, because mirroring and rotating yields the original, thus no other versions. (See the table to the lower right of the poster for examples.)

Rules for sorting
The poster groups variations according to the number of non-overlapping rectangles. The large figures indicate the beginning of each group. The sequence begins in the upper left and proceeds from left to right and top to bottom. Each group is further divided into sub-groups sharing the same set of elements. The sub-groups are arranged according to the size of their largest element from largest to smallest. Squares precede rectangles of the same area; horizontals precede verticals of the same dimensions. Within sub-groups, variations are arranged according to the position of the largest element, preceding from left to right and top to bottom. Variations themselves are oriented so that the largest rectangle is in the top left. Black dots separate groups by size. Gray dots separate groups by orientation.

Where to learn more
Grids have been described in design literature for at least 50 years. French architect Le Corbusier describes grid systems in his 1946 book, Le Modulor. Swiss graphic designer Karl Gerstner describes a number of grid systems or “programmes” in his 1964 book, Designing Programmes. The classic work on grids for graphic designers is Josef Muller-Brockman’s 1981 book, Grid Systems.

Thomas Gaskin and Sean Durham have created an interactive tool for viewing variations and generating HTML. www.3x4grid.com

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Patch Kessler explores the mathematical underpinnings of grid generation in his paper “Arranging Rectangles”.

The 892 ways to partition a 3×4 grid from thomas gaskin on Vimeo.

Examples and a good description such as those described by Gowan and Novak (in Learning How to Learn) are helpful for understanding concept mapping. An exercise in which you make a simple concept map (with eight to 12 terms) may also be helpful.

The first step in concept mapping is to generate lists of words related to the main concept. The list can come from research, reading, experts, brainstorming, or any other source. Sharing lists from members of a development team will help generate other words.

The second step is to edit the list. Some terms may be related to the subject, but not in a way that meets the project goals.

The third step is to define the terms on the edited list. This is particularly important with unfamiliar or technical terms. But it also helps with familiar terms, too.

A useful exercise is to create a matrix listing all the terms down one side and repeating the list across the top. The relationship between the terms is noted in the boxes where a row and column intersect. The resulting matrix of relationships provides a checklist for building the concept map.

Another important step is ranking of the terms. Simple “triage” may be sufficient. Some terms are key to defining the concept. Others are clearly details. Some fall in the middle. The ranking provides a way to begin to look at building a structure. Primary terms may be candidates for an armature sentence.

One approach is to ground the primary concept within a sentence that also contains the other two or three most important terms. A first sentence might set context; a second sentence might define the main term branching out at 90 degrees from the first sentence. The armature sentence provides a starting point for the map. From there, you can add secondary terms and then the details.

Another approach, is to look for a structure or model to underlie the concept map. For example, brand is a type of sign. Signs have three components. Those three components become the anchor points of the concept map. Innovation is a process which repeats, oscillating between convention and innovation. The process provides a structure for the concept map.

Making a concept map in an area that is well defined is sometimes fairly easy — if the information space can easily be found and if most authorities agree on it. For more ambiguous topics, a great deal of time may be needed to agree on scope (which terms are in or out) and on structure (how those terms relate). This process can take several weeks or even several months.

Once the terms and structure are agreed to, you can move to a second phase: giving the map an appropriate typographic form — to make the typographic hierarchy support the structure of the content.

Main steps in creating concept maps:

• List terms
• Edit the list
• Define the remaining terms
• Create a matrix showing the relations of terms
• Rank the terms
• Decide on main branches or write framing sentences
• Fill in the rest of the structure
• Revise
• Apply typography to reinforce structure
• Revise

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Created in collaboration with Jack Chung, Shelley Evenson, and Paul Pangaro.

The creative process is not just iterative; it’s also recursive. It plays out “in the large” and “in the small”—in defining the broadest goals and concepts and refining the smallest details. It branches like a tree, and each choice has ramifications, which may not be known in advance. Recursion also suggests a procedure that “calls” or includes itself. Many engineers define the design process as a recursive function:
discover > define > design > develop > deploy

The creative process involves many conversations—about goals and actions to achieve them—conversations with co-creators and colleagues, conversations with oneself. The participants and their language, experience, and values affect the conversations.

See also our How do you design? collection of models.

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Created in collaboration with Satoko Kakihara, Jack Chung, and Paul Pangaro.

This model is built on the idea that play is a type of conversation. It involves two individuals, who might also be teams, or points of view with in a single person, or a virtual person and a real person. Through conversation, they create a shared world in their imaginations, which leads to fun.

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Created in collaboration with Sean Durham, Ryan Reposar, Paul Pangaro, and Nathan Felde.

This model is built on the idea that innovation is about changing paradigms. The model situates innovation between two conventions. Innovations transform old into new. It is a process—a process in which insight inspires change and creates value.

Read the Interactions Magazine Article which explains the process of creating the map.

See also our collection of Innovation Models.

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Increasingly, organizations are focusing on understanding their customers to increase customer satisfaction and to maximize lifetime customer value. Insights gleaned from observing customers can drive product improvement, loyalty, word-of-mouth referrals and cross- and upselling.

Created for CIO Insight magazine, this diagram decodes current methods of customer tracking, retention, and acquisition. It shows the relationship between customer data, touch points, behaviors, data capture systems, customer databases, data integrity, customer segmentation, lists and targeted offers. The goal of the diagram is to provide a model of how organizations today track customers to retain them longer and acquire more.

Read the CIO Insight Magazine Article which accompanies this map.

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Created in collaboration with Paul Devine.

The domain name system stores and associates many types of information with domain names, but more importantly, associates domain names (computer hostnames) to IP addresses. DNS is a system vital to the smooth operation of the Internet.

The goal of this diagram is to explain what DNS is, how it works, and how it’s governed. The diagram knits together many facts about DNS in hopes of presenting a comprehensive picture of the system and the context in which it operates.

Hugh Dubberly created this diagram in conjunction with a study: “Internet Navigation and Domain Name System.” The study was run by The National Academies’ Computer Science and Telecommunications Board which convened a study committee. The study was sponsored by the Department of Commerce and the National Science Foundation and mandated by the US Congress.

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Created in collaboration with Audrey Crane.

For many years, Stanford University Cardiac Rehabilitation Program (SCRP) has conducted research on ways to change the behavior of patients who have had heart attacks. Their research is aimed at reducing the risk of a patient having another heart attack. Educating patients and their families is a key component of changing patient behavior.

Working under contract with the American Heart Association, the Stanford team asked DDO to help them develop a master plan for a new education program. DDO developed a series of prototypes of an integrated communications program involving print, video, and online components. One print component, a Health Coach notebook for patients (images below), included educational material, including this concept map. In this map, a patient can quickly see what a heart attack is, its causes and risk factors, and most importantly, behavior that can reduce the risk of a heart attack.

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Created in collaboration with Audrey Crane, Jim Faris, and Harry Saddler.

This diagram explains Java by placing it in the context of related concepts and examples, and by defining its major components and other connections between them.

The diagram is intended to help developers who are familiar with one part of Java understand other parts. It relates unfamiliar technologies to ones with which developers may already be familiar. The diagram also provides an overview for developers who are new to Java and an introduction for non-programmers who want to improve their ability to converse with developers.

The completed map contains approximately 235 terms, 425 relationships, and 100 descriptions.

We also created a Flash version of the map.

Read the article Using Concept Maps in Product Development: Preparing to Redesign java.sun.com.

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This diagram is a model of brand, a term often used in business, marketing, and design. The diagram attempts to present a comprehensive model of brand and to unpack the meaning of the term by providing related concepts and examples. You read the armature of the map (structure) horizontally and vertically. The map is framed around four main ideas:

1. a brand is more than a name or symbol
2. creating a great customer experience is the essence of good branding
3. perceptions of a brand can be measured
4. brands are a form of sign

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