Simulations suggest that one can build a device that computes upon echoes of clicks of a dolphin and that displays an image of what that dolphin is acoustically "seeing."

May 2016: Fish-Finder in 3D, a potential application of my methods.
C S

November 2016. I have, since 2014, programmed more simulations and been writting a few new patent-applications.

The latest, June 2014.

I have untangled this mystery: it had dawned on me that in my latest simulations, redone to demonstrate Feature-Based Passive (FBP) methods, my arrays were of much smaller diameter than the previous ones - and I had very little clue what I had done to make this possible. I have solved this mystery and can now show how to make a sonar-array - for imaging (still falling short of the detail that dolphins seem capable of) from echoes of clicks of real dolphins - the size of which array is about that of the chin of a bottlenose dolphin.

August 2014 / June 2015.

New insights have destroyed my "narrative." I am developing new explanations, involving new terminology. Also, I am changing the patent-applications that I had in progress.
Summer 2015. I am writing the strategic patent (application) that I call "Synchronics."

Mathematics of the Sonar of Dolphins

This new computational method is called "feature-based passive," or "FBP," sonar.
The methodology enables computation of an image from a single "click" like that of a dolphin. The waves used for imaging are not limited to sound. Ideas for applications include
* the world's best fish-finder
* imaging objects that are buried under sediments
* rapid, lower-cost, 3D imaging of the interior of the human body
* deep seismological imaging of the interior of Earth (from orbiting satellites)
* analogous radar applications.

The new approach to computing images from waves has been inspired by the Echotrigger/Scopion Theory of the imaging sonar of dolphins. But the mathematics applies to waves other than those of sound and so a new name, "wavar," has been adopted to refer to the general principles.

Wavar, here, is being developed using "experiment-machines" -- simulations software for rapidly crafting and running experiments that probe for information in waves.

The approach, here, is "geometric" in that its calculations use geometry and not sophisticated methods of analysis such as Fourier analysis.

The new (I think) and simple signal-processing methods herein can reasonably be called "feature-base passive", FBP, in that they use times-of-arrival of known features of particular waves and cn use, but do not require, knowledge of time and place of emisssion of those waves.

You can click here to a simulation from 2005 that portrays two fish seen from 50 feet above as they cavort about each other. The animation represents the possible functioning of a first version of "the world's best fish-finder."

It seems that in most species of toothed whale, for which sonar-clicks have been recorded and graphed, the clicks all have one prominent instance of a feature called a "fang."

Geometric methods seem likely to have advantages in speed, in cost, and in rante.

Geometric methods are seriously limited in the detail of their images. Other methods, using thin beams of transmitted waves can "see" into nooks and crannies not visible to broad-beamed geometric methods.