Color theory as a framework for class-based and fuzzy-based uncertainty

Encoding uncertainty via the visualization is a common approach in virtual archaeology. Basically, one takes the information from the documentation and applies it to the previously described model. In return for that, various approaches have been established, although the color code is by far the most common method.

Firstly, there is the color gradient. In this research and many others, it is used to display numerical values along a scale. This best corresponds to fuzzy-based uncertainty. With the used brown to red gradient, several aspects can be covered at once. It is:

• Intuitively comprehensible. Brown stands for uncertain areas while green covers certain areas.

• A complementary pair of colors.

• Able to connect successfully a numerical value to a color value. • Robust against most color blindness.

111 However, when using a smooth gradient, utilities are necessary to determine the exact value since the difference might be too subtle to be detectable by sight. A stepped gradient that groups the scale into value ranges could be a solution (fig. 54; fig. 56). However, it also increases the inaccuracy of the measurement. Considering the results of the case study (fig. 51), the assignment of a color gradient works smoothly. Nevertheless, the result is slightly different than expected.

Instead of a three-dimensional reconstruction with a color gradient, a reconstruction similar to the class-based approach is achieved. The only difference seems to be the actual colors themselves. Since the gradient is not visible anymore, it loses all of its significance. One reason might be the clustering of similar values among similar segments. However, even with regard to this peculiarity, it is difficult to recognize a gradient. A possible way to counteract this might be the reduction of the colors used. Instead of using complementary colors, only monochromatic colors (fig. 59) could be used. The monochromatic colors have their variation in brightness instead of color. Since the priority is to maintain the behavior of a gradient, this might be the best solution.

Figure 59: Comparison of a monochromatic gradient (left) indicating the uncertainty of a Mayan temple relief (Schwerin 2016, 213) and a complementary gradient (right) indicating the uncertainty of several columns (Kensek et al. 2004, 178).

In contrast to the gradient, the harmonic tetrad can be used for the class-based uncertainty. The harmony consists of four complementary colors. They are all assigned the same distance from each other at the color wheel. In theory, that is the best way to indicate contrasting opinions. However, the opinions are not always contrasting in this case study; they can also be supportive. One could solve this by bringing the colors closer together and thus weaken or strengthen the contrast. Despite the change of the color

112 meaning, this process would be highly speculative and not eligible for scientific research. Nevertheless, Sifiniotis et al. 2007 determined the impact of several classes on scholars in a survey. This survey might serve as rough outline. Likewise, when reducing the classes to three active ones, primary colors (fig. 60) can also be used. However, they might form a harmony, but no complementary contrast. Blue and green are too close to each other. A solution might be the substitution of either green or blue by another color. Likewise, they could be assigned to related classes. For example, the class fieldwork and analogy both describe actual structures. Therefore, both classes contain similar data and might be more closely related to each other than to illustrations. However, if the primary color green is used for the fieldwork and red for illustration, there might be the intention of a red and green contrast, which in this case would be undesirable. Still, primary colors can be helpful in solving cumulative or fluctuating uncertainty. They offer the advantage of being known and are easy to distinguish from each other. Furthermore, they are seldom found in natural environments and can be easily mixed with each other. Basically, they form the root of the color theory, in which the classes will form the root for the uncertainty theory.

Figure 60: Concept of color mixing at the source classification. The colors of two categories can be mixed. The ratio relates to the impact of each color. Primary colors are used as a base, which will transform into secondary colors – right circle (Brunke 2017).

The only problem with primary colors is their intrusiveness, and inauthentic harmony and complementarity (fig. 60). Improvements of perception can be made by adjusting the brightness and saturation. Likewise, tiny bits of other colors can be added. Further improvements will be made if the color classes are mixed with the color gradient. A two- parted scale can deal with fluctuating uncertainties, as well as with cumulating.

To sum up, each classification will have been assigned one complementary color. Each of the color classes receives a subscale with differing brightness representing a relative or absolute subscale of uncertainty. In cases of several sources, the two representing colors can be mixed together (fig. 60) in accordance with their influence on the interpretation.

113 The emerging color will be the actual complementary color of the color class that is not used in this process. For example, fieldwork (red) and analogy (blue) are mixed. In an additive system they will result in a kind of purple, which is the complementary color used for illustration (green). This can further exclude or include parts of the discussion. The new color is now called a secondary color. They can be easily broken down into their individual single colors. To display different weightings in the argumentation, the mixture ratio of those two colors can be adapted. The exact value can be then easily measured with a color picker or the modeling software used to determine the ratio.

Material libraries that can be created for Blender are especially suitable for this purpose and they can be used in multiple projects simultaneously. Those are usually based upon easy shaders or textures. More complex patterns might require physically-based textures. The principle of physically-based textures can be also transferred to the uncertainty concept and used for encoding different types of uncertainty within one material. Each segment then becomes an extra piece of material assigned for each uncertainty instance. The user can switch and render the most convenient or requested one.

In short, complementary colors and the class-based uncertainty concept are better suited to revealing the nature of the source, whereas gradients and fuzzy-based uncertainty can easily display values. Considering the results of the case study (fig. 51), it might not even matter which concept is chosen since both forms of visualization feature similarities. They might look similar, but the highest information density can only be reached in a mixed approach for both of them, namely using color classes as containers for the rough framework, and color gradients for a subtle scale with fine details. To cover even the outer extreme of the scale, additional render modes can be added as described in the next section.