1. FRACTAL DIMENSION OF ELECTRON prof. Ing. Pavel Ošmera, CSc. Brno University of Technology osmera @fme.vutbr.cz MUDr. Pavel Ošmera – junior Department of Imaging Methods, Faculty of Medicine of Masaryk University St. Anne's University Hospital Brno osmera @fnusa.cz June 27-29, 2012 MENDEL 2012

2. Intoduction We would like to find a better and plausible structure of the electron as a torus and fractal structure. However it is in contradiction with generally accepted knowledge, where the electron has not a structure. Actual properties of the electron cannot be explained by point-like models. This paper is an attempt to improve our previous calculations of the radius of the electron and its fractal dimension. The vortex-fractal theory could possibly help with explanation what the charge, the electron, the proton, the electromagnetic field, etc. actually are.

3. Main ideas and differences MENDEL2010

4. a) spiral structure as the fractal-spiral structure b) fractal-ring structure Fractals seem to be very powerful in describing natural objects on all scales. Fractal dimension and fractal measure, are crucial parameters for such description.

5. a) b) c) Vortex structures: a) the vortex V B at the drain hole of bath-tub, b) the vortex tornado-vortex V T c) the vortex in the PET bottle

6. MENDEL2009

7. The fractal ring structure of the electron MENDEL2010

8. The spin of the electron Vortex structures with spin 1/2 MENDEL2010 MENDEL2012

9. The fractal ring structure of the electron MENDEL2007

10. . MENDEL2012

11. Fractal dimension of the electron where N is number of substructures (number of new sticks), ε =1/S is scaling factor, N 1 = N 2 = 42

12. MENDEL2007

13. The spin of the electron MENDEL2012

14. r 1 = 0.7223517245r o ~ 0.382Å, r 2 = 1.792517214r o ~ 0.948Å the couple constant α

15. Structure the of hydrogen atom

16. Structure the of the neutron proton electron

17. Conclusions Fractals seem to be very powerful in describing natural objects on all scales. To understand the electromagnetic field requires a high degree of imagination. The degree of imagination that is required is much more extreme than that required for some of the ancient ideas. The modern ideas are much harder to imagine. We use mathematical equations and rules, and make a lot of pictures. We can’t allow ourselves to seriously imagine things, which are obviously in contradiction to the known laws of nature. And so our kind of imagination is quite a difficult game (or a puzzle). One has to have the imagination to think of something that has never seen before, never been heard before. At the same time the thoughts are restricted or limited by the conditions that come from our knowledge of the way nature really is. The problem of creating something which is new, but which is consistent with everything, which has been seen before, is one of extreme difficulty. Treating the electron as a torus structure rather than the point-like particle is a very challenging.physical topic.