Multi-Beam Interference Patterns of Living Sarcoma Cells may be Approximated by a Fractal Julia Set and Rieman Spheres or Fatou Components Decoded as a Siegel Discs

Abstract

It’s well known, that the morphology of a carcinoma cells was studied many a time and oft (on repeated occasions) from the second part of the XX century. But mathematical approximations of such sarcoma cell structures are not very good on the grounds of non-regular semi-chaotic elements in morphogenesis and morphology of cancer cells. Many approximations in sarcoma oncology works are not applying for cell morphology as is, despite the fact of good morphological representation of sarcoma cells in different microscopic and specific-staining methods. Our work is a first work where the multi-beam interference patterns of living sarcoma cells are approximated by a fractal Julia set and Fatou components known as a Siegel discs.