Vasubandhu’s Treasure of Abhidharma
Vasubandhu’s Treasury of Abhidharma describes the inhabited world as a circular disk resting on elemental layers of earth, water, and wind. At the center of the world is an enormous mountain, called Meru or Sumeru, surrounded concentrically by successively smaller oceans and mountain ranges. In the last peripheral ocean rest the four main continents of the world, including our realm of Jambudvīpa. The edge of the world is formed by the Cakravāla mountain range.
Wheel of Time (Kālacakra)
The Buddhist Wheel of Time texts describe an alternative view of the world with distinctive structural principles. For example, the elemental substrata are reflected repeatedly in the colors and shapes of the continents and the colors of the facets of central Sumeru.
For more, see Creating the Universe.
Vajradhatu Mandala (Vajradhātu maṇḍala)
Ritual Order and Architectural Installation
This image illustrates the different spatial sequences in which figures of the Vajradhatu mandala are invoked in a Newar (Nepalese) version of the ritual. For more, see Image and Text in Newar Buddhist Ritual Manuals.
A variant of this mandala may also be constructed in receptacles inside a caitya. For more, see Creating the Universe.
Mandala Offerings (Newar and Tibetan)
Offering the mandala is one of the fundamental rituals of Vajrayana Buddhism, frequently encountered as part of guru puja or lama chopa. Although it generally involves creating a small model of the cosmos to give as a gift, its performance varies in different traditions.
To start with, the offering may be performed in 5, 7, 13, 17, 21, 23, 25, or 37 parts, expressing various kinds of mandalic symmetry.
In each version, the order of placement of the parts of the offering naturally differs, as does the list of items that make up the complete offering. Illustrated below are a seven-part version, the twenty-one-part Newar version, and the thirty-seven-part Tibetan version.
The following table lists groups of items used in the thirty-seven-part Tibetan offering.
Perhaps the most common way to offer the mandala during a ritual is by gesturing with the hands, having the fingers represent the central mountain and four major continents of the world.
During the ritual, the mandala is also invoked in speech, with particular syllables representing each part of the offering. The following diagram lists the Sanskrit syllables spoken in the Newar ritual and delineates four groupings of related syllables in the four directions.
Samye (bSam yas) Geographies
Originally constructed during the first diffusion of Buddhism into Tibet, Samye monastery (third from left in diagram) exemplifies a complex and multilayered geographic symbolism, invoking aspects of cosmology (far left), mandalic space (second from left), local and transcontinental political relationships (top right), and spatialized embodiments of teaching (bottom right).
For more information, see Layered Cosmologies in Himalayan Buddhist Shrines.
I have also produced illustrations of non-Buddhist topics, including some for an exhibition of ancient American ceramics that are available here.