From then on, I wanted to do just one design that could stand unashamed alongside those of The Master.

How hard could it be? ...   H’mmmmm ... ?   Where do you even start?

Later, around 1996, after doing a few tesses myself, I recorded this feeling in rhyme on my website:

Once I saw a sketch by Escher: Sky and Water is its name
It’s Ducks and Fishes actually, but precious just the same.
Those beasties blew my brainbox – I was never so impressed:
So then I  tried to tessellate – Put Escher under pressure, Mate! –
Well, excel those at any rate: to better Escher’s best!

(It continues, as you may see on my site.)

It took me until 1993 to manage even one respectable tess, and then it happened not by effort but by a chance perception ...

... One day I was at a boring meeting, doodling stick-figure Kangaroos, and suddenly I saw that the space above the back and tail of a west-facing Kangaroo could neatly fit the southern coast of Australia’s map. Then I found that three more, with persuasion, could define the Eastern, Northern and Western parts of our coast.

It took a lot of re-drawing: my technique is to use a soft (2B) pencil: I’m left-handed (as was Escher) and my handwriting is horrid! I do many light spidery lines which can easily be erased without damage to the paper using BluTack (that’s a hint folks!), making successive approximations of ideal shapes. Hundreds and hundreds of lines, until I find the best I can. That was my technique then and remains so today. But in the end, to my delight, I had a very creditable translational tessellation which I called OZZIE the Magic Kangaroo, remarkably marrying Australia’s twin icons, even including our baby Island State of Tasmania. And I loved it! (See it on my site.)

I didn’t even know then that tesses were of interest to mathematicians. But then, a complete stranger named Paul Scott, Professor of Pure Maths at Adelaide Uni, rang me to enquire about it. I don’t even know how he heard about it, but anyway, the upshot was that in 1996, at his invitation, I wrote the centrefold article about it in The Australian Mathematics Teacher, a very well-thought-of educational magazine of which Paul was Editor. My experience eerily echoes Escher’s own, where he records that, having been largely ignored by the Art community in Holland, he found his way from a beautiful but lonely “garden” of his own kind of art to “the open gate of mathematics” through which he passed to acceptance, and eventually to eternal international acclaim.

And in my case, that recognition by Prof Scott, the realisation that tessellation was so much more than decoration, encouraged my interest as never before.

Kangaroos had not finished with me — they still haven’t! For the Sydney Olympics in 2000 I drew and re-drew them in many sporting poses — skiing, boxing, high- and long-jumping, playing basketball, riding a bike, archery and more! And in the process I found a handful of other Kangaroo tessellations, some of which you may see on my own site – and one, TwoRoos, was The One I had always wanted.

TwoRoos fulfilled my every personal demand: it is my favourite type of tessellation, a “glide reflection”, of my favourite animal, basically very true-to-life, in its iconic position, i.e. full but relaxed flight. That is the one on this Tiled.art site, and Thank You Very Much Rick!

By then I had become even more fascinated by figurative tessellation generally, and gradually my little menagerie grew to include Elephants (which are remarkably obliging), Koalas, Seahorses and more, including some designs which are not animals: maps of Australia itself, Plane Tree leaves (for the pun on ‘regular division of the plane’! ... though the erudite Maths Teacher and author Jill Britton, a Canadian, thought they were Maple! ); and so on.

Unfortunately for me, I am a mathematical ignoramus, and I am not at all handy with graphics programs either. My “technique” for designing tesses, if it can be termed that, comes not from grids or patterns to start with, but from perceptions of possibilities in random shapes ... markings on bark or blobs of squashed chewing gum on pavements or crumpled kitchen paper or cloud formations ... I remember Escher’s son telling of how his father would pick out suggestive animal shapes on a stuccoed wall in their bathroom and accentuate them for the rest of the family’s entertainment. I imagine that some of his tesses found their origin in that way. So my painful quest for any given design starts at total chaos, and progresses to absolute order – I guess a shrink would be able to draw some conclusions about my mind but anyway that’s how it is. If I find a feature that keys with something that looks interesting – e.g., a Kangaroo’s head with another’s front paws and belly – I torture the animals to try to make them fit all around, which mostly physical laws of nature insist that they only do with extreme difficulty, if at all.

But when they do, it’s marvellous.

And then and only then is when a regular pattern emerges, and at last I perceive the underlying grid.

I don’t wish to do endless numbers of tesses: I try to make my victim creatures as lifelike and proportionate as possible, which severely limits my subjects: it tends to preclude cartoonish graphics for me. I avoid straight lines, as computer graphics often involve; I don’t do fantastic creatures like winged dragons, while big hair and flowing clothing to fill space are not acceptable. And there are now so many tesses of birds, fishes and dogs that I am not interested in adding more, though I’ve done a few of each myself. Australia has provided me with many unique creatures which few others have attempted: Platypus, Koala, Leafy Sea-Dragons, Numbats, Cockatoos, so many others! I always try to show all 4 limbs of quadrupeds, plus other prominent features such as big ears and tails. That’s not easy: many tesses of horses or dogs have only 3 or 2 legs visible, which I find a bit unsatisfying. With Kangaroos, as you may see, I was lucky: for one thing, Escher didn’t try to tessellate any (he would’ve probably found TwoRoos if he had!) and for another, Yes, Kangaroos are quadrupeds but their legs operate in unison, in pairs, so in profile they look like they are two-legged, plus tail. As in that beautiful Penny image.

One cannot invent  tessellations, if you see what I mean: the design you bring to light has always been there waiting to be discovered. But once discovered and defined it is eternal!

What is it about tessellations anyway?

Whence this strange power to fascinate mathematicians and artists alike, and even those not usually interested in art or maths?

Why are Escher exhibitions nowadays, fifty years after his death, always crowded with people of all ages, genders, educational levels, staring, ooh-ing and ahh-ing?

Is it because everyone everywhere would like everything to fit  perfectly, in every sense?

Is it because of the implication of infinity in every tessellation, which would gladly extend beyond the stars if given an endless plane to play on?

Is it because you’re wondering ... ???! How in the world ...???

If I had to offer a technical psychological explanation, I would say that it’s because the duality inherent in every line animates and tickles our usually somnolent and cynical schizophrenic nerve. That nerve can’t quite believe it, and in some people, it itches like mad. I know because I’m one of them. At 79 I’m still fascinated, and still attempting the odd tessellation, right now one of mummy ’Roos with joeys, one of pretty fan-dancers!

— Bruce Bilney

P.S. I do indeed love tessellations, but my first love is rhyming verse because only language conveys thought. Much of my verse is eco-educational – those animals I’ve tessellated are always close to my thoughts, and I’ve managed to combine my facility with verse with my much-lower-proficiency with drawing, as you may see on my site. Most of my graphics on that site have a verse to keep them company.

Confidentially, I think that what might have been the section of my brain that should have been learning about Mathematics (and money) spent so much time with lines running around in my head, with homophones and scansion and emphasis and that sort of ilk, that it atrophied ...

But I do I recommend you read Klokan the Blue Kangaroo to children. It’s actually pretty nice.    ... Show less