This is the fourth in my series (rapidly becoming a weekend tradition) of presenting 4D solids as art. Today’s offering is called a “Dini Surface”. In geometry, Dini's surface (named after Ulisse Dini) is a surface that can be created by twisting a pseudosphere (an object with constant negative Gaussian curvature). Think of a pseudosphere as the opposite or inverse of a sphere (which has positive Gaussian curvature). If you could see today’s rendering in motion, you would see an object forever disappearing into itself. This piece is a freeze-frame of that action. Now, you may be thinking, how could something disappear into itself forever; it would just do it once and vanish. But that is like asking how could you rotate a sphere forever; you could only do it only once and no more. By analogy, the Dini Surface can disappear into itself forever in the same way that a sphere can be rotated forever (only it is the inverse of a sphere rotation). A sphere rotates positively; a Dini Surface rotates negatively. Cool huh? D. H. Lawrence once said: ~~Design in art, is a recognition of the relation between various things, various elements in the creative flux. You can’t invent a design. You recognize it, in the fourth dimension. That is, with your blood and your bones, as well as with your eyes~~ Created in Ultra Fractal