If the yin loop of space-time quantum is denoted by lowercase letter ‘y’ and the yang is denoted by uppercase letter ‘Y’ then they can be used to formulate a yin-yang algebra of their interactions as follows.

In the fractal dimension of ½, both the binary operations of addition and multiplication can be applied: Y+Y=2Y, Y+Y+Y=3Y, y+y=2y, y+y+y=3y, but y+Y=0. The last expression implies that y and Y are additive inverse of each other with the additive identity 0. On the other hand, multiplication gives yY=2y, YY=2Y, yy=2Y, 0y=y0=0, 0Y=Y0=0, yyy=4y, YYY=4y, yyyy=8Y, yYY=4y. The multiplicative identity and inverse are not defined. Therefore, the set of all y or the set of all Y is defined as a semi-ring. The union of two semi-rings forms a complete ring and a complete ring is always a binary combination of y and Y or among themselves taken 2 at a time preserving the commutative property for both addition and multiplication.

Applying this algebra to elementary particles gives the following ring leaders: an electron is 7y1Y, a photon is 4y4Y, a neutrino is 1y1Y, an up quark is 1y5Y, a down quark is 3y1Y, and similarly all the other particles can be represented. The space-time charge of y and Y is determined by addition. The space-time mass is determined by multiplication. The absolute value the space-time charge for each y or Y is always 1/6. On the other hand, their masses depend on their fractal dimensions. For example, in the fractal dimension of 1/6, the bare or naked mass of the electron is 6=279936. This is a dimensionless number, while that of a proton is 6. The mass ratio of proton to electron is then 2 times 6. It square root is approximately 1832, an error of about 1/5 of a percent of the experimental value 1836. This can be attributed to the magnetic moment of the particle configuration.