30th September 2012
The "fractal" modulation [0, 8 , 10, 6, 10, 8, 0] cm is based on the depth sequence of the stepped diffuser [0, 4, 5, 3, 5, 4, 0] multiplied by 2. Why? Because it was a simple modulation to try without making the diffuser too deep, and it performed well when tested in Reflex.
There are many possible modulations, and [0, 5, 6, 4, 6, 5, 0] cm might also work.
These profiled modulations were found through experimentation. I could supercharge the process using the design by optimization system, which I used to create the base shapes... but that would take time to set up, run and verify...
If you did not mind a thick diffuser, you could create a low frequency fractal stage (a profiled modulation) with the proportions equal to the stepped diffuser (i.e., keeping the width:depth ratio consistent, where width:depth ratio = 42 cm/5cm = 8.4). Considering an array of 7 diffuser modules (294 cm wide), the deepest step of the profiles modulation would be 294 / 8.4 = 35. Since the deepest step of the stepped diffuser is 5cm, you would scale all the depths by 35 cm / 5 cm = 7.
This would give you a profiled modulation of 7x[stepped diffuser depths] = [0, 28, 35, 21, 35, 28, 0] cm... resulting in a much deeper diffuser than the one we started with!