Shells and Exclusion Lines

Instead of starting from a time series with n number of samples I decided to investigate the DFT as the number of samples built, starting at zero and increasing. Of course there isn’t anything at zero, so I start my plot by putting a small zero at the centre. Somewhere between zero and one is the event horizon, a place you can’t see in to. You don’t get to see until the first sample. If there is just one sample, the phasor plot appears as in Figure 5. The zero point is represented as a black circle, the initial condition, the sample as a red dot. Wherever there is a sample I draw a line from the origin passing through and emanating from the sample dot. I call this the exclusion line. The circle tracing the path of the sample I call a shell, so Figure 5 shows the 1 shell. When the number is prime I call it a Prime shell.