Why does this redstone pulser circuit produce this result?

Solution 1:

A comparator has 2 modes

Compare mode (torch unlit):

• Check if the signal coming in from the back is greater than or equal to the signal strongest signal from either side.
  • If yes, emit the power of the back side to the front side
  • If no, emit no power to the front

Subtract mode (torch lit):

• Check if the signal coming in from the back is greater than or equal to the signal strongest signal from either side.
  • If yes, emit the difference in power from the sides vs the back side to the front side
  • If no, emit no power to the front

In your case, you made a loop of 7 redstone wires long to the side of the comparator.

Lets assume you just placed a lever behind the back of the comparator, and that you just turned the lever on. (this is like your last example)

1. The comparator (compare mode) now receives a signal of 15 from the back, and 0 from the sides. It will emit a signal 15 the next tick.
2. The comparator (compare mode) now receives a signal of 15 from the back, and 9 (15 - 7 + 1) from the sides. It will emit a signal 15 the next tick.

As you can see, a comparator in compare mode is "stable", lets toggle the mode

3. The comparator (subtract mode) now receives a signal of 15 from the back, and 9 (15 - 7 + 1) from the sides. It will emit a signal 6 (15 - 9) the next tick.
4. The comparator (subtract mode) now receives a signal of 15 from the back, and 0 (6 - 7 + 1) from the sides. It will emit a signal 15 (15 - 0) the next tick.
5. The comparator (subtract mode) now receives a signal of 15 from the back, and 9 (15 - 7 + 1) from the sides. It will emit a signal 6 (15 - 9) the next tick.
6. The comparator (subtract mode) now receives a signal of 15 from the back, and 0 (6 - 7 + 1) from the sides. It will emit a signal 15 (15 - 0) the next tick.

This doesn't look very stable at all...

Using the values, we can also explain what the trap doors are doing.

• The trap doors in the green region are between 0-6 tiles away from the comparator, meaning they always see the full signal
• The trap doors in the yellow region are between 6-15 tiles away from the comparator, meaning they see the signal going on and off quickly
• The trap doors in the red region are between further than 15 tiles away from the comparator, meaning they never see the signal

The lamps take 2 ticks to turn off, meaning they don't react quickly enough for the fast clock.