Louisa S. Cook's Geometrical psychology, or, The Science of Representation: An Abstract of the Theories and Diagrams of B. W. Betts details Benjamin Betts' remarkable attempts to mathematically model human consciousness through geometric forms. From the Introduction:

The symbolic forms which Mr. Betts has evolved through his system of Representation resemble, when developed in two dimensions, conventionalised but very scientifically and beautifully conventionalised leaf-outlines. When in more than two dimensions they approximate to the forms of flowers and crystals. .... The fact that he has accidentally portrayed plant-forms when he was studying human evolution is an assurance to Mr. Betts of the fitness of the symbols he has developed, as it affords presumptive evidence that the laws he is studying intuitively admit of universal application.

After living in India for a spell, Benjamin Betts, who was educated in England as an architect, obtained a post as “Trigonometrical Computor of the Survey Department” in Auckland, New Zealand’s Civil Service. But he moonlighted as metaphysician, developing a “Science of Representation” based on Johann Gottlieb Fichte’s remark, in The Science of Knowledge, that lines and circles might correspond with modes of consciousness. Not everyone understood his ideas, however: Betts wrote a letter to John Ruskin, enclosing his illustrations, who replied with a chastisement: art must be spontaneous. But it was not art that Betts was aiming for and he found a better correspondent in Mary Everest Boole, the self-taught mathematician and wife of the late George Boole.

The images featured here both refer to what Cook calls “horn-shaped corolla”, one classified as “Ond” and the other “Onde”, alpha and omega forms of the “animal sense-consciousness which underlies the human or rational sense-consciousness”. The corollas are expanding and open because, according to Cook, this is how Betts thought the ego functions:

This progressive qualification of consciousness is represented by the Onde, as the progressive quantification of consciousness is by the Ond. The latter starts from a centre of possibility and extends itself ad infinitum into objectivity. The former starts from an objective circumference absolutely limited for the time being, and qualifies itself subjectively ad infinitum. Thus a complementary form of consciousness is evolved, a form contingent on the evolution of the first form. The Ond may be called the form of the Intellect, and the Onde the form of the Emotion of a rational ego on the sense plane.