The Golden Ratio's Siblings

On real numbers whose fractional part remain constant after squaring.

Click here to read my paper.

I Heart Mathematics

Saw this on the web recently and thought it was cool.
Instead of using $\pm\frac{4}{5}$ for the y-intercept though, the golden ratio φ = $\frac{1\pm\sqrt{5}}{2}$ should have been used for a more natural beauty. Also, what would the equation be in 3D?