Mathematically, the program visualizes real algebraic geometry in real-time. The surfaces shown are given by the zero set of a polynomial equation in the variables x, y, and z. All points in space that solve the equation are displayed and form the surface. As an example look at x2+y2+z2-1=0, the equation of a sphere. You can easily see that the point (x,y,z)=(0,0,0) is not on the sphere while the points (1,0,0), (0,1,0) and (0,0,-1) for example solve the equation. The program includes a big sample gallery with explanations and a tutorial. It is available in several languages including German, Spanish, Russian, Serbian, and Portuguese.

The great thing about SURFER is that you don’t have to understand the underlying mathematics (algebraic geometry) a priori, you can experiment, try, follow your intuition and creativity and this way learn maths and create unique artwork like pictures or animations.

SURFER is the new, Java-based version of the program SURFER2008 that was developed for the IMAGINARY exhibition in the year of Mathematics 2008 in Germany. The program is platform-independent and runs on a Windows, Linux or Mac operating system. SURFER has been used for many IMAGINARY exhibitions and is constantly improved and extended.

NOTE FOR MacOS users: the SURFER app is not notarized. Please follow these instructions to override your security settings to open it (you will see a warning dialog).

NOTE for Windows users: in newer Windows versions, necessary DLLs are missing (msvcr100.dll) and they need to be installed to run SURFER. You can find the runtimes here under the title “Visual Studio 2010 (VC++ 10.0) SP1“ (we installed both 32 and 64 bit just in case).