This ancient Aztec technique is one of the most regenerative and productive forms of agriculture throughout history and can be adapted for use in a number of ways. Aztecs used this method to feed a massive civilization from a relatively small area of land. They did this by integrating soil fertility and pond life habitat together in a very symbiotic way.
They dug a series of finger channels near the shore, stabilized them with willow tree roots or posts, and grew corn, beans and squash and other nutrient loving, calorie dense crops on the berms. They would drive fish into the channels and trap them in the channel, making fishing much easier. The beds always had access to water when they needed it, and the water was full of fertility from fish poop and other organic matter from the pond.
Some chinampas were made from reed islands, receiving fertigation directly to the roots - a precursor of modern day aquaponics.

There are many ways to use the chinampas concept.

These chinampa variations could be used in wet landscapes. Similar approaches have have been used for centuries in Asia to grow rice.

With all the lakes and swampy areas in Florida and elsewhere, chinampas could be a very viable way to increase the yield from these areas. Keep in mind, that lakes and especially swamps have their own functions in ecosystems and watersheds, and if we destroy those functions with our agricultural methods, whether through chemical poisons or through “permaculture” earthworks, we are not practicing regeneration.
Note how little of the shoreline the Aztecs used to feed their populations.
The watering system I designed in our gardens used some of the concepts from the chinampas system. I put fish in our water tanks, and they were open, so I also caught organic material which ended up as fertile soil in the bottom of the tanks. The water used on the gardens had fish waste and other organics in it. When we flood irrigated, it looked like a temporary chinampas. This was also true during a heavy rain.