Measuring the fractal wavelength


An attempt to measure the fractal wavelength.
Rational
This entry came (to me) from working on the fractal spiral, the fractal wave, and de Broglie demand curve entries. As it is impossible to measure both time and distance, it may be possible to measure - even if only in principle - the distance of the wavelength - based on a known dimension, the length of the triangle side (l).

Background.
Fig. 1 below shows the fractal and its (while developing) 'wave-like' nature. It shows that the wave takes 6 iterations to repeat or produce one cycle, but it does not show the length of the wave or its wavelength (λ).


Fig. 1 

Measuring the wavelength is an experiment.
It occurred to me that the wavelength (λ) may be measured or at least better understood through a simple experiment.
Method:

  1. Take the iteration 0 triangle and post it on a wall. 
  2. Cut the iteration 1 triangle from the fully developed Koch snowflake from a paper print. 
  3. Hold the paper at arm's length and sight the triangle 0 through the triangle 1 hole.
  4. The arm length will be known as a standard observation distance* 
  5. Move forward or back with the paper extended at a standard distance, and find the place where triangle 0 appears the same size as triangle 1. 
  6. Make a mark of this distance.
  7. Repeat the process, this time for triangle 2, and mark the distance. 
  8. Repeat the process for triangle 3, and mark the distance. 
  9. Record the distances (in metres), then divide these distances by the triangle base length.
*There is an issue with the 'standard distance': The accuracy and, thus, validity of the distances measured in processes 6,7,8 and 9 are dependent on the standard distance, and as this distance is subjective, there is a measurement problem. Thus, there is no standard distance.
More to come.

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