Generative Flowers as a Language of Forms for the Visualization of Binary Information

In the past few decades, fractal methods have become common in generative art. Such methods can be applied to data visualization, yielding generative objects open to interpretation in terms of a data structure. Various authors have proposed approaches based on botanically inspired Lindenmayer fractals [1] and related methods [2-5]. The method I propose here makes use of nonlinear fractal trees [6], which are bent as a function of the information present in a given bit string. I analyze the string by moving a p-bit window over it and determining coefficients for each of 2^p strings of length p. The latter strings are associated with the leaves of a tree with 2^p end-nodes, and the coefficients of these strings determine the curvature in the branches of the tree.

Before it is bent, a tree-representation has to be initialized. An initialization is appropriate if the spatial structure of branches gives visual information about the p-strings attached. This can be realized if the initialization of the tree is a highly structured and familiar form. In Color Plate E, I use the boundary of the Man-delbrot set to initialize a tree.

After a tree is bent by data, I turn it into flower form. This is carried out in two steps. First, I interpolate endpoints with a contour. Second, I project this contour in a series of steps so that a surface is obtained. The projections are defined by successive small variations of the parameters associated with the tree. More concrete or more abstract flower forms result, depending on the choice of parameters. In an alternative method, the flower is generated and does not envelop the tree, but is put at different times on top of the leaves instead. The spread of the flowers over the leaves of the tree-as well as their attributes "size" and "open/closed"-are based on information derived from p-bit analysis (Color Plate E).

This procedure can be applied to bit strings that appear in fundamental domains such as one-dimensional cellular automata and tag systems (which figure in discussions about fundamental aspects of our world and our knowledge [7]), or to visualize the properties of bit strings that occur in more applied domains, such as genetics or musical composition. If music is encoded in a long bit string over which a bit window is moved that is in turn analyzed in terms of smaller p-bit windows, a moving visualization results in which the tree structure is transformed continuously and the flower canopy on top of it widens and shrinks, and for which flowers continuously open and close as a function of musical progression.