Chaos and GraphicsEvaluating Second Life for the collaborative exploration of 3D fractals
Introduction
Two-dimensional (2D) fractals have generally been studied more than three-dimensional (3D) fractals and their generation is supported by a number of software packages, such as FracInt [1]. In contrast, exploration of higher dimensional fractals requires a more sophisticated 3D user interface, more complex visualization techniques, and places higher demands on capabilities of the graphics hardware. As a result, softwares that allow one to study 3D fractals are far less common and often written by individual researchers. Alternatively, 3D fractals are created within general purpose rendering/modeling packages in which the fractals are either created manually or by using an internal scripting/programming language to automate what is often an iterative or recursive procedure. These software tools are often available only for a particular computer platform, are often relatively expensive commercial packages, or are geared towards an interactive representation of fractal geometries for a single user. As a result the process of conveying and sharing a sense of the 3D geometry is relegated to the production of precomputed 2D projections, namely, rendering images or movies. Even these 2D projected representations are generally not presented as a real-time collaborative experience but a delayed-in-time file exchange through email and web pages.
By contrast, multiplayer games by their very nature (at least for first person shooters) allow participants to engage directly and interactively with 3D geometry within a virtual world. They are generally designed for a broad audience and as such are available for a number of operating systems, are easy to install, and have a well-designed user interface. Additionally they tend to exploit the capabilities of modern graphics cards to achieve the highest visual quality for a target frame rate.
Second Life is an online 3D virtual environment managed with a server–client software model and created by Linden Labs [2]. In addition to participants being able to create and modify their assets in virtual environments, Second Life provides a rich environment for social networking [3]. Indeed this is perhaps the most engaging activity for many participants. These characteristics mean it has also been explored for collaborative learning experiences [4]. The discussion here then is to determine to what extent Second Life can be employed to represent and convey 3D fractal geometries. Most construction activities within Second Life involve manual creation of buildings by choosing from the rich set of geometric building blocks provided (boxes, prisms, spheres, etc.). This construction occurs by using what is essentially a built-in 3D modeling system. This manual building process can be applied to the iterative/recursive nature of most (but not all) 3D fractals, but fortunately there is also a built-in scripting language that can be used to automatically construct 3D forms. The evaluation then largely consists of determining to what extent the Linden Scripting Language (LSL) of Second Life [5] can be used to create some of the classical 3D fractals. Only actual 3D fractals will be considered. Image or geometric fractals that are only 2D can be explored collaboratively with simpler video conferencing tools that generally support image sharing through whiteboards, for example.
Section snippets
Evaluation
The first classical 3D fractal to be considered is the Menger sponge, first described by the Austrian mathematician Karl Menger [6]. This is certainly an object that can be created manually quite easily with Second Life modeling tools. One begins with a single cube, duplicates it 27 times in a 3×3×3 grid, then removes the cube in the center of each face and center of the entire grid. This resulting collection of 20 cubes is then grouped together and considered to be the cubic element to which
Conclusion
While Second Life provides a cross platform and highly engaging virtual environment that can represent many 3D fractals, there are clear limitations. It should be pointed out that an attempt is being made to use software for a task it was not necessarily designed to perform. In most cases the limitations identified exist for pragmatic reasons and are intentional in order to give a satisfactory user experience across a range of hardware and network capabilities. The strengths of Second life
Acknowledgement
The author acknowledges the Bowling Green State University for providing a sand pit that supports a large number of primitives. Much of the exploration here would have otherwise been less efficient.
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