The inspiration for making crochet reef forms begins with the technique of “hyperbolic crochet” discovered in 1997 by Cornell University mathematician Dr. Daina Taimina. The Wertheim sisters adopted Dr Taimina’s techniques and elaborated upon them to develop a whole taxonomy of reef-life forms. Loopy “kelps”, fringed “anemones”, crenelated “sea slugs”, and curlicued “corals” have all been modeled with these methods. The basic process for making these forms is a simple pattern or algorithm, which on its own produces a mathematically pure shape, but by varying or mutating this algorithm, endless variations and permutations of shape and form can be produced.
And, yes, they have a how-to book if you’d like to try this on your own.