Hi, I’m David Bailey from Grimsby, England, with a keen interest in recreational mathematics, of a mostly geometrical nature, and more specifically of tessellations along with their application to polyhedra. This website is thus dedicated to showing my own efforts in this field, along with some other aspects pertaining to the subject.

As such, the tessellations are overwhelmingly of the ‘representational’ type i.e. of animal-like motifs as exemplified by the Dutch graphic artist M. C. Escher (1898-1972), although this is not to say that I have no interest in the purely geometric aspect, it’s simply that the former is where my strengths and inclinations lie, resulting from an inherently artistic background. In broad terms, artists and mathematicians whom are drawn to tessellations tend to confine their studies to their respective domains, and so, perhaps somewhat unusually, I have an active interest in both types, although without doubt I do indeed concentrate my studies towards the representational aspect.

As such, the 'acid test' of a representational tessellation should be its realism to what it is supposed to be portraying. As such, I believe my tessellation to be of a high quality in this matter - all too often, I am sorry to say, I see tessellation websites where too little time, thought or attention has been put into the ‘creative process’, resulting in ‘representational tessellations’ that leave a lot to be desired, to say the least. Regarding the quality of my own tessellations, some very learned American mathematicians have taken an interest, such as Prof. B. Grünbaum (U. Washington) ‘…in the hope of seeing more of your work’ and Prof. G. E. Martin (U. New York) ‘If you are willing to share your constructions, I would like to examine them in more detail...’ (The latter in connection pertaining to studies of hypermorphic tessellations.) Suffice to say, as regards their inherent quality, I consider that the above thereby speaks for itself.

The tessellations shown are mostly of what I term as of final, definitive examples, drawn and coloured (generally of watercolour) by hand, and not a computer. These are essentially the product of a systematic study, which frequently belies various complexities that of necessity require a thorough approach. Also included are some that are best described as studies, of which, for various reasons, I have simply not found the time to complete as finished examples. These are thus simply denoted as ‘study’. Generally, but not always, the definitiive tessellations are accompanied by some explanatory text, whereby the various ‘intricacies’ behind the tessellation are discussed. In addition, each drawings colouration is discused. Although such matters are not in any way essential to appreciating tessellation, only by a full 'revealing' of its intricacies will its merits be truly appreciated. In contrast to this, I frequently see tessellation websites with no such background detail, consisting solely of pictures only, and so the viewer is left to ponder its merits unassisted. Admittedly, not all tessellation websites have drawings of quality worthy of explanation, but even so, at least some explanation, even if relatively minor, would be welcomed.

The tessellations here are so placed into distinct groupings as according to their motif, i.e. of birds, fishes... as appropriate, with any further subdivision, due to there being so many examples of a specific motif (primarily of the bird examples) are thus put into arbitrary subcategories for the sake of general order.

New for November 2005:

1. Additional text discussing the tessellations
As a rule, more text has been added, along with each finished work having a discussion as to its colouring. (Previously, the colouration of each drawing was discussed somewhat arbitrarily, if at all, essentially according to whim.)

2. How Escher did...
A new section, in which I show how Escher achieved certain effects of 'Black, Grey and White', 'Development' and the aforesaid 'In Combination'.

3. Development
A new section, of finished motifs, in which principles of development are shown.

4. Essays on artistic media
A new section, primarily aimed for those unfamiliar (such as mathematicians) with artistic matters.

5. Rearrangement of essays on M.C. Escher's drawings, prints and 'miscellany'
These are now shown in a more 'convenient' form, in smaller sections. (Previously, these were in a single PDF format for each of the three groupings).

6. Rearrangement and new, additional material of 'aspects' of tessellation, in distinct sections.
These are now shown in a more 'convenient' form, in smaller sections. (Previously, this was in a single PDF format. titled Aspects and Processes of Creating Representational Tessellations.)

The next update will be March 2006, with further updates planned on an approximately four-monthly basis.

Contact Click Here

David Bailey

Revised 14 November 2005.