AN INTERACTIVE VIRTUAL ENVIRONMENT TO LEARN CHAOS

Many researches show that learning by non traditional methods is a successful experience. Virtual Reality technologies allow creating visual and auditory environments that can be used for science education and dissemination.
This paper describes a virtual environment used to present the fundamental concepts of chaos theory. These scientific topics are very suitable to be shown by using innovative educational simulations allowing users to employ the underlying mathematical models in a creative manner.
The virtual environment was created in occasion of an exhibition about generative arts based on chaotic system and it was especially designed to allow novice to learn advanced scientific topics through a visual and audio virtual trip.
The environment is made up of four different sub-sections: interacting with the attractors, spatial sound experimentation, the attractors collection, experimenting the sensitivity to initial condition.
In the first section, using game-like input devices (i.e. joystick), users can explore the 3D scene seeing the chaotic attractors, the characteristic chaotic trajectory, and listening to the sound and the music generated from their evolutions. Users can also interact with the chaotic system used to generate the attractors. By changing the parameters of the mathematical model that simulate the chaotic system, they can explore how this affects its evolution and the resulting shape of the attractor. The interaction with the chaotic systems allows users to experiment with a deep exploration of the behaviors of the attractors, exploiting the richness and the beauty of their shapes by using both visual and auditory representations. Moreover users can employ the chaotic system in creative manner improving their scientific knowledge and stimulating their critical interest and creative ways of thinking.
In the second section, users can experience 3D spatial sound listening to the audio spatialised according to the evolution of 3D mathematical curves and chaotic attractors. To do this, we used a sound system made up of eight speakers placed at the corners of a cube that allows simulating the positioning and the movement of sound sources in 3D space.
A collection of ten different attractors is presented in the third section. Here users can experiment the richness of shapes and behaviors provided by the chaotic system by moving around the trajectories and listening to the sound that each one generates.
In the fourth section, an experiment about sensitivity to initial condition is presented. Two attractors are generated starting from two different initial conditions, each differing from the other by a very small quantity. At the beginning and for a short period of time the attractors seemingly evolve according to the same trajectory, but after a while the small initial difference is amplified and each attractor follows its own trajectory. The evolution of each attractor is transformed into a sequence of notes played by a certain instrument. Initially only one melody is heard because the attractors follow almost the same trajectory, but eventually, two distinct melodies, played by different instruments, are heard.
The paper presents a description of the virtual environment architecture and a detailed explanation of the four sub-sections. Moreover the tools used to create the virtual environment will be presented as well as the results provided by the analysis of the feedback supplied by the visitors of the exhibition.