Dear John Larkin,
I like that one! It's notably simple, as in being a DC-to-DC converter having only 4 components (excluding the often-advised capacitor across the power supply leads of the IC - .1 uF 25V cheapie ceramic capacitor is an often-advised occaisionally-necessary item that gets the component count up to 5, 6 if you also count the LED.
Component count may get to 6 excluding the LED, 7 including it, if this boost converter gets good enough to overpower the LED or deliver more output power than desired, so as to necessitate adding a resistor in series with the LED.
I would like to add that efficiency is likely to improve if the non-LED diode (a reaistor is offered as a workable alternative) is a Schottky one. I would look into Schottky diodes with breakdown voltage 30V at most, maybe 20V, and rated to handle 1 amp or less, maybe much less. Come to think of it, much less to get improvement towards shorter switching times.
It does appear to me that the shown capacitor and resistor are "left to the student". I would like to make that capacitor .01 uF merely from knowing that one is a common cheap part. I could gain desire to make it smaller in consideration of likely oscillation frequency considering a desired value for the shown resistor...
I would want to make that resistor 100K max to "make this cleaner", and I have a liking to get oscillation frequency into the 50 to mildly-above-100 KHz ballpark, in order to make the oscillation frequency ultrasonic to humans and most pets (even though dB acoustic pressure is impressively low to negligible likely less than 30 1 meter away).
Also I would want the oscillation frequency to be not-too-close to the common ones for TV/VCR/DVD common consumer devices. But if the LED emits at a shorter wavelength, as in/near blue, that is less-likely a problem. If that problem comes up anyway, I would primarily put a longpass filter in front of the consumer device sensor - as in Wratten preferably 92, secondarily 29, tertiarily 25 or equivalents including Schott glass longpass optical filters (regardless ofwho supplies longpass optical filters based on Schott glass products), having part numbers starting with RG and including afterwards 630 to 670.