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Painting Algorithm Using Cell Developmental Mechanism

Sezin HwangAssociate ProfessorFaculty of Mobile Contents, Daegu Haany University, Daegu, Korea

Moon R. Jung[footnoteRef:1] [1: Corresponding Author. This work has been supported by the Sogang University Research Grant of 2011.]

ProfessorGraduate School of Creative Media, Sogang University, Seoul, Korea

AbstractIn this paper, we present a painting algorithm that generates paintings by a mechanism analogous to cell developmental mechanism. In our system, basic shapes with position, size, and color play the role of cells. Starting from a single cell, children cells are generated from the parent cell, and the generated cells are arranged with one another by means of simple rules. The rules determine the attributes of children cells, e.g. their color, size, and displacement from the parent cell. When the development is finished, the cells are drawn in various figures, such as circles, lines, and circular arcs. By adding randomness to the attributes of children cells, the algorithm produces paintings that have unpredicted moods with various shapes and colors. Also, unlike traditional painting that mixes color pigments, this painting method creates unpredictable colors by mixing colors directly. The color addition effect is significant especially when thousands of shape elements are overlapped.

1. Introduction

This research aims to look at painting from a new perspective, that is, by means of computational capability of computer. In computer arts, computers are often used as software editing tools for creating shapes or images. The authors, however, believe that employing computer programming directly without using an editing or modeling tool is a worthwhile approach to creative computer arts. In particular, we want to employ cell developmental mechanism for the purpose of shape generation. All living things in the world are generated by means of cell developmental mechanism. So, it would be interesting to see what happens when we apply this mechanism to painting.

In this algorithm a basic shape element acts as a cell. And the first shape is divided as in cell division, creating numerous shape elements that have various sizes, colors, and positions, and a painting is created by combining them. Each cell is divided when it is grown to become as twice as the original size. When a cell is divided from the parent cell, its position, size, and color is determined in its relationship with the parent cell. When numerous cells are overlaid upon one another, the colors are mixed and create unpredictable colors. When a cell is drawn in this algorithm, it is drawn in various basic figures such as circles, lines, and circular arcs.

2. Background

The first case of using computer for artwork was arguably paintings produced by computer algorithms. From the mid-1960s, scientists and artists tried such projects, and some of them called themselves algorists[footnoteRef:2]. [2: http://www.algorists.org/algorist.html]

2.1 Harold Cohen Cohen is an artist who used to be recognized as top 5 British artists in the late 1960s, but suddenly stopped painting and started developing an artificial intelligence-based automatic painting system called Aaron. Cohen, by creating an Expert System[footnoteRef:3], made a freehand line drawing program. The rules of Aaron were inspired by childrens doodling styles. Aaron starts to draw a figure from an arbitrary point on the canvas and stops when an adequate number of figures are drawn.[footnoteRef:4] is an example of such drawing. Different drawings are created each time due to random aspect of the painting system.[footnoteRef:5] [3: An expert system is a program that expresses knowledge of an expert by using a number of If...then... else rules to solve a given problem.] [4: Harold Cohen (1988), "How to Draw Three People in a Botanical Garden," Technical Report, University of California, San Diego.] [5: Pamela McCorduck, AARON'S CODE: Meta_Art, Artificial Intelligence, and the Work of Harold Cohen ( W.H Freeman and Company, New York, 1992)]

Aaron materialized the traditional genre of line drawing with artificial intelligence and was expanded to draw concrete forms.

2.2 Growth Model of Kawaguchi Yoichiro (Growth Model) Kawaguchi, by using a method called growth model, has visualized developmental process of life forms[footnoteRef:6]. Growth model algorithm starts from the initial form and grows and regenerates it, by repeatedly applying simple rules. This growth algorithm uses a genetic algorithm. The result of the growth algorithm is represented in constantly moving animation and is a snapshot. Growth model continuously creates an abstract life form starting from the initial form. The present study aims to create pure abstract painting using only forms and colors in the framework of traditional painting. [6: http://design.osu.edu/carlson/history/tree/kawaguchi.html]

2.3 Automatic Geometric Abstract Painting by A. Michael Noll In 1965, Noll had the first computer art exhibition in the US with Bela ulesz at Howard Wise Gallery[footnoteRef:7]. Noll was highly interested in the unpredictability of drawings created by computer and recreated artworks of existing painters. is by Mondrian, who is well known for geometric abstract painting. is a drawing produced by using random numbers of computer. One hundred participants received a paper in which and were printed on one paper and asked to distinguish the one generated by computer. 59 out of 100 participants judged , which was generated by computer, to be Mondrians actual painting, and only 28 chose , the artwork by Mondrian.[footnoteRef:8] Noll argued many people who participated in the test linked randomness to human creativity and confused it with Mondrians painting[footnoteRef:9]. Nolls algorithm painting does not allow intervention by an artist and many of his works (Figure 5, 6) use simple black and white geometric forms and lines. For interesting composition, the present method allows direct involvement of an artist and various combinations of geometric forms and colors. [7: Frank Dietrich (1986). The First Decade of Computer Art (1965-1975), Vol.19, No.2, 159.] [8: A. Michael Noll (1996), Human or Machine: A subjective comparison of Piet Mondrians Composition with Lines(1917) and A computer-generated picture, The Psychological Record, pp1-10.] [9: A. Michael Noll (1967), The digital Computer as a creative medium, IEEE Spectrum, Vol.4, No.10, pp89-95.]

The differences between several existing studies and the present research are shown in .

3. The Decision Rules of Cell Attributes

3.1. Composition Rule In this work, a simple cell developmental mechanism is used to generate painting. In general, rules that compose a painting include so many elements[footnoteRef:10]. However, in this work we want to use simple rules to see what they produce when they are repeatedly applied. We introduce three simple rules for determining the attributes of children cells derived from parent cells. [10: David A. Lauer & Stephen Pentak (2005), Design Basics, Sixth Thomson Wadsworth : According to Design Basics, which is widely used as a textbook for basic design education in universities in South Korea and elsewhere, elements to compose a design include unity, balance, emphasis, focal point, scale, proportion, rhythm, line, shape, volume, texture, and illusion of space, illusion of movement, brightness, and color. ]

In the process of devising composition rules, Kandinskys painting of has been examined carefully. A child cell is defined by three attributes, as shown in : (1) the size of the cell, (2) the color of the cell, and (3) the displacement from the parent. The rules are designed so that the size of a child cell is determined in inverse proportion to the size and color brightness of the parent cell, and the color brightness of the child cell is determined in inverse proportion to the color brightness of the parent cell, and the displacement from the parent is determined in proportion to the difference between the color of child cell and the color of the parent cell. These are simple and intuitive rules designed so that shape elements forming a painting should be balanced in their attributes, such as size, color, and displacement, rather than being one-sided in these attributes.

3.2. The Rules Determining the Attributes of Children Cells

3.2.1. The Decision Rule of the Child Cell Size

The child cell size is determined to be in inverse proportion to the size of the parent cell for the following reason. If the parent cell is big, the feel of its presence in the painting is strong. It is reasonable for the child cell to have a weak presence and so be small. If the parent cell is small and has a weak presence, the child cell is made big so that the cells as a whole have some balance in size. The child cell size is determined in inverse proportion to the brightness of the parent cell as well for the following reason. If the parent cell is dark, it has a weak presence. It is reasonable for the child cell to have a strong presence and so be big.

3.2.2. The Decision Rule of the Child Cell Color

The brightness of the child cell is determined in inverse proportion to parent cell brightness for the following reason. When the parent cell is bright, the child cell is made dark, and vice versa. It is to make the brightness of the parent and child cells in balance. The brightness of the child cell does not uniquely determine its color. So the color of the child is determined by randomly choosing a color whose brightness matches the given brightness.

3.2.3. The Displacement from the Parent Cell

The displacement between the parent and child cells is expressed in terms of rotation and translation in 3-dimensional space.[footnoteRef:11] The rotation is determined randomly while the distance from the parent is in proportion to the difference between the child cell color and the parent cell color. In other words, when the difference in color is small, the displacement of the child from the parent is made small, and vice versa, in order to avoid putting contrasting colors close together. [11: Sumanta Guha (2011), Computer Graphics Through Opengl, CRC Press ]

4. Painting Algorithm

4.1. Overview of the Algorithm

Each cell is represented as an object in the programming language (a script language called Python)[footnoteRef:12], and the attributes of an object include the color, size, displacement from the parent object, and the list of the children objects linked to the object. Through this children list, the algorithm visits the children objects of a given object and perform various actions on them. The flow of the algorithm is shown in . Each cell grows until it becomes double the original radius. Then the cell divides and produces a child cell. [12: Allen Downey (2008), Think Python-How to Think Like a Computer Scientist, Green Tea Press, ]

4.2. The Decision Rules of Cell Attributes

4.2.1. The Initial State of the Parent Cell

For the development-based painting algorithm, the initial state of the root cell must be given. The color of the root cell, that is, the R, G, B, A[footnoteRef:13] values are randomly chosen between 0.0 and 1.0 and the maximum cell size is set to be 40[footnoteRef:14]. The position of the root cell is set to be (0.0, 0.0, 0.0) so that it is right at the center of the global coordinate system. The initial size of the canvas is set at 500x500 pixels. The initial setting can be adjusted. [13: Four channels of 32 bit graphic system. A refers to Alpha channel.] [14: The units of measurement used in 3-d computer graphics are arbitrary, and only the relative relation is important. However, it can be thought of in terms of' cm or m for conveniences sake.]

4.2.2. The Decision Rule of the Child Cell Size

As explained in Chapter 3, the child cell radius is set to be in inverse proportion to the parent cell radius, and the parent cell brightness. The child cell size is obtained by using the following formula.

Formula 1.

Formula 2.

Formula 3.

shows that the size coefficient of the child cell is in inverse proportion to the ratio between the parent cell radius and the maximum cell size, and the parent cell brightness of . Here, the parent cell brightness is the average value of (). shows that the size of child cell is determined y multiplying the size coefficient of by the parent cell radius. shows a flow chart for determining the child cell radius.

4.2.3. The Decision Rule of the Child Cell Color

The child cell color is randomly chosen after first determining the child cell brightness.

Formula 4.

Formula 5.

The brightness coefficient is determined according to so that the child cell brightness is in inverse proportion to the parent cell brightness. The child cell brightness is obtained by . If the parent cell is bright and has a strong presence, the child cell has a dark color and a weak presence, and, if the parent cell is dark and has a low presence, the child cell is made bright so that it has a strong presence. It is to make the parent cell and the child cell are balanced in brightness. shows a flow chart for calculating the child cell brightness.

The color of the child cell is expressed as (). The value of the child cell () is set to be in inverse proportion to the value of the parent cell by . The child cell color () is chosen randomly among the colors that has the same brightness as the child cell brightness obtained by .

Formula 6.

Formula 7.

Formula 8.if

elif

else :

The child cell color () is determined by the rule described in . First, select a random number by using f = random ( )[footnoteRef:15]. f becomes a random number between 0 and 1. If f < 0.33, of the child cell color is chosen randomly, and, if f < 0.66, of the child cell color is chosen randomly. And is determined by using the brightness condition. shows a diagram for calculating the color of the child cell. [15: Function random( ) creates a random number between 0 and 1.]

4.2.4. The Decision Rule of the Displacement from the Parent Cell The displacement from the parent cell is expressed in terms of rotation and distance. The distance is determined by a given rule, whereas rotation is chosen randomly. The distance between the child cells from the parent cell is set to be in proportion to the distance between the child cell color and the parent cell color. The color distance coefficient is set as follows:

Formula 9.

When the color distant coefficient is obtained, the distance between the parent cell and the child cell is calculated by

Formula 10.

Here, basicDistance is the distance between the centers of the two cells.

Formula 11.

If there is a large difference between the child cell color and the parent cell color, the child cell is located far from the parent, and if there is a short distance, the child cell is located near the parent. This is to place cells with similar colors close and cells with contrasting colors far from one another, in order to reduce the feel of contrast between the parent and the child. shows a flow chart for calculating the displacement from the parent.

4.3. Morphological Expression of Cells

4.3.1. Shapes of Cells

In this algorithm, to draw a cell, a polygon expressed by is used. Specific polygons are defined by specifying the parameters and in . This algorithm uses four forms of cells. A sequential number is assigned to each cell as a cell id, each time they are created. If the cell id number modulo 4 is equals 0, the first cell form is drawn, if the cell id number modulo 4 equals 1, the second form is drawn, and so on.

Formula 12.[footnoteRef:16] [16: Fletcher Dunn, Ian Parberry (2001), 3D Math Primer for Graphics and Game Development, CRC Press]

In , when a > b, it looks like an oval long in the direction of the x axis, and when a < b, long in the direction of the y axis. Especially, larger difference between a and b creates an extreme oval which looks like a line segment.

4.3.2. Examples of Cell Shape When the parameters are set as in , we obtain a polygon as shown in .

Formula 13.

shows the result of painting by overlaying 3,000 polygons of this form.

Formula 14.

As another example, a polygon drawn by creates a polygon as shown in . When three different cell shapes are used and 1,200 polygons are overlaid, the result is .

4.4. Blending of Cell Colors

When the proposed algorithm generates and draws numerous cells, many cells are overlapped in position. In this case, the colors of the cells become blended. In OpenGL programing, blending is performed automatically if the blending function is set in advance. If the initial background image is given for the frame buffer, each time a new image is drawn, the color blending between the current frame buffer image and the newly drawn image takes place according to the given blending function.

5. Conclusion

In this paper, we have described a painting algorithm that uses a simple cell developmental mechanism. It is analogous to developmental mechanism in which cells are divided and an individual creature is developed. The painting algorithm proposes an intuitive algorithm that determines the color, size, and displacement of a child cell relative to the parent cell, when the child cell is divided from the parent cell.

In the beginning, we had some doubts that an interesting painting would be generated by a development-based algorithm, but the result was surprising. An extremely interesting paintings were by generating and combining basic shape elements according to three simple decision rules. Although the algorithm is basically automatic, the paintings were made with an active involvement of the author in setting the parameters of the algorithm. In this sense, it is differentiated from conventional automatically-generated paintings. It is a new painting technique available to artists who know how to do computer programming.

Figure 1. Aarons Line Drawing 1979

Figure 2. Kawaguchi Yoichiro, 1996, soft seaweed moving in the sea, or a result of growth model algorithm that resembles swimming unicellular organism.

Figure 3. Mondrian, Composition with Lines, 1917

Figure 4. A. Michael Noll, Computer Composition with Lines, 1964. Composition of Mondrians lines regenerated by a computer

Figure 5. A. Michael Noll, legend opposite, 1965.

Figure 6. A. Michael Noll, Kinetic Sculpture, 1960s.

Figure 7. Several Circles 1926.

Figure 8. Visual grammar of Several Circles. In this painting, the colors, sizes, and relative distance among circles seem to be the most distinct attributes.

Figure 9. Tree structure of the algorithm. (1) the root cell divides cell 1 and takes it as its child. Fig. : the root cell divides cell 2 and takes it as its cell along with cell 1. Also, cell 1 divides cell 3 and takes it as its child; cell 3 and 2 do not have a child and nodes without a child are leaf nodes.

Figure 10. Deciding child cell radius .

Figure 11. Calculation of brightness coefficient and child brightness

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Figure 12. Calculation of child cell color.

.

Figure 13. Calculation of displacement from parent cell.

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Figure 14. Expression of

.

Figure 15. Result of painting by overlaying 3,000 polygons from

.

Figure 16. Polygon from

.

Figure 17. Result of painting by overlaying the polygon from and 1,200 polygons of three different shapes

.

Table 1. Characteristics and Difference of Existing Studies.

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Artist/SystemCharacteristicsCharacteristics of this study

Aaron by CohenAutomatic painting system using the expertise of the artistLine drawing with concrete formsAlthough the artists knowledge is used, the painting is abstract and geometric in form

Growth Model by KawaguchiVisualization of developmental process of a life form artificial life formsPure abstract painting created only with forms and colors

Geometric abstract automatic painting by NollArbitrary recombination of empirical knowledge of existing artistsSimple geometric black and white forms Various geometric forms and color combinations by active involvement of the artist