Mathematica is the tool used to create all of the images in this and other Graphica books. Mathematica is a software system--an environment for technical computing--originally designed by Stephen Wolfram as a tool for exploring ideas in science, technology, and elsewhere. Mathematica was first released in 1988, and in the years since that time it has become the tool of choice for well over a million scientists, engineers, financial analysts, students, and others. Mathematica has been used to design airplanes, to manage fisheries, to analyze stock markets, to discover important new science and mathematics, to solve innumerable homework exercises--and also, almost from the beginning, to create art.
Mathematica incorporates vastly more facts about algebra, trigonometry, calculus, and other fields of traditional mathematics than any human has ever known--or is likely ever to know. And it can use these facts to do in seconds calculations that would take humans months or years to do unaided.
But the essence of Mathematica is its language for describing and manipulating expressions. The Mathematica language was designed from the start to provide a clear and precise way of communicating ideas--from human to computer or from one human to another. Computer languages typically specify the operations in a rather low-level and literal way. But Mathematica is essentially unique among languages in common use because it operates at a much higher level, a level corresponding much more closely to normal human thinking.
All sorts of people use Mathematica to do all sorts of things. Sometimes people use Mathematica like a calculator, asking it mathematical or other questions and letting it use its internal capabilities to work out the answers. Sometimes people use it like a notepad to record and organize their thoughts and ideas. And sometimes people use Mathematica and its language to specify ways to create forms of all kinds. A rich set of graphics objects is available to assist this kind of visualization. These graphics objects can be created, transformed, combined, and manipulated within Mathematica with ease.
In the past decade many of the technological objects that we use--and the scientific advances that those are based on--have been created using Mathematica. In the decades to come, the Graphica series points the way to a new generation of artistic forms created using Mathematica.