No. Mathematica is a creation of Stephen Wolfram: Wolfram Mathematica: Modern Technical Computing Spirix is something I created to create mathematical mesh surfaces in SketchUp (along with U-V PolyGen).
Mathematica is not “open source” … however, all of my own code may be used freely and can be downloaded from my code site: spirixcode
Hope you don’t mind that I “stole” your idea with the glass swirls and made a render:
