Evolutionary Fractal Art
School: Sat Sci Math Acad
Area of Science: Computer Science, Biology
Interim: Using Fractal Art to Define Beautiful Images
Defining “beauty” is based on user perception, interpretation, and preference. No single definition exists, but by observation we can assign weight to attributes that allow us to predict what the larger population may determine to be attractive. Of the three types of models we can employ, we seek to predict a model that is consistently appealing to the larger population.
As a solution to the problem we plan to have multiple people rating fractals using an interactive website. The fractals will evolve based on human preference, each user with their own population. For evolving the fractals we plan to use three different approaches in reproduction. Asexual reproduction, Sexual reproduction with random pairs, and Sexual reproduction with user specified pairs. All three approaches will differ but will also be similar enough to be comparable. Each approach will have the same population size and the same number of fractals in each generation. From our website we plan to collect data to figure out what approach and method to the problem is the best. For the most accurate data we plan to have many people rate fractals and track how the fractals evolve in each method. To keep users rating fractals as long as possible our website will be entertaining, fast paced, and interactive.
Progress to Date:
To date, we have created a web site that allows users to choose two seeding fractals; “x” and “y”. After selecting the initial fractals, a child is generated and displayed in the web application. Web2Py (www.web2py.com) supplies the application framework and Python programming libraries used to support our application. We are using Apophysis7x (apophysis.xyrus-worx.org) to generate the fractals. Fractal definitions are stored in XML for human readability, manipulation, and the ability to export in data in the future. Spawned children combines attributes of the parent fractals stored in a new XML file.
We anticipate that of the three model types, asexually generated models (slight deviations of a common seed) may not offer enough diversity. Sexually-generated models (random pairing of parent seeds), may offer too wide a variance. We predict that new fractals generated based on previous images judged to be appealing (by humans) will produce better images overall. As beauty can be subjective, we believe we can supply empirical data (via a higher preference) to define what a human may deem attractive. Using this definition, we can create a mathematical formula (algorithm) to produce additional images humans find attractive over the first two models. To avoid bias, individuals who supply input in generating the seed images will not judge spawned children. “GIGO” (Garbage In, Garbage Out) is a term used in computing to express the output is only as good as the input. We will use this principal to input “Quality In” expecting “Quality Out” (QIQO); thus mathematically giving definition to beauty.
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Sponsoring Teacher: Debra Johns
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