Books

Books about basic techniques

See the Processing web site for an extensive list of recommendations of material specifically related to using Processing.

They do, of course, recommend the "Processing Handbook" by Casey Reas and Ben Fry (the people who invented Processing). It is certainly a convenient reference book to have by the computer when you are working, though you will find pretty much equivalent reference material on the Processing web site. (Though in fact it does not contain all the reference material. You will still need to refer to the Reference section of the website.)

I still find this book useful, though I would call it a luxury purchase. It is not at all essential, but some of the interviews with digital artists may give you new ideas.

I also like the book Generative Design, by Hartmut Bohnacker, Benedikt Gross, Julia Laub, and Claudius Lazzeroni, because it contains lots of inspiring examples and is beautifully produced.

The Processing site, however, has all the essential reference information and also an Exhibition area which an extensive range of intriguing artworks. Nevertheless, there are many advanced techniques (such as building random fractal landscapes) that are not part of the basic tutorials.

If you are still exploring generative art in a year or so, you will find an extensive literature and lots of free extensions to Processing to use as building blocks.  However, be warned:  “advanced” means tools that rely on more understanding of the underlying concepts. There is plenty of guidance out there, but you do have to engage brain.

Books about Symmetry

Creating Symmetry: the Artful Mathematics of Wallpaper Patterns is something different. It investigates the complete set of different types of symmetry patterns that can occur and explains the mathematics. It also uses the theory to generate images showing the various types of symmetry. A degree of mathematical sophistication is required to follow the mathematical explanations.

A very good pre-university maths student would follow quite a lot and learn quite a lot that would be a good foundation for 1st-year university maths - but they would need determination. In order to read it reasonably fluently you would need the type of daily practice with mathematical ideas that only comes after working with university-level maths. (Indeed, the book was produced for maths students at an American university). As with learning a foreign language, it is one thing to have passed your high-school exams and quite another to read fluently.   

You can just look at the pictures and gain some understanding of symmetry without the being able to use it to generate the more sophisticated patterns. However, I suggest that you only lay out your money if you have a sound mathematical background. If you do, then it is well worth the trouble of working through this book. Patterns can be a lot more complicated and interesting than you might think!

I have had this book for many years (from shortly after its publication in 1992) but only recently rediscovered it on my bookshelf when searching the Web for further reading on connections between maths and art. Memories were roused when I read a review of this volume and I was sure that I had seen it before - and eventually convinced myself that it was somewhere on my disorganised bookshelves.

It investigates connections between symmetry and chaotic dynamics. The authors have also developed computer software to produce the spectacular images in the book.

On Growth and Form by D'Arcy Wentworth Thomson is a classic of theoretical biology on natural forms and patterns first published in 1917 (subsequently revised and extended several times) and has been in print every since, though sometimes in abridged versions. It has long been recommended reading to students in a surprising variety of disciplines apparently unrelated to biology including architecture and software engineering. (The ideas of pattern and form are treated in a way which turns out to have resonances wherever designers need to give complex structures underlying unity.) the book is interesting in itself, and very well written, but it is also full of diagrams that may well inspire digital constructions.

Beware! Some of the cheaper modern editions now on sale are very heavily abridged versions of the 1000-page original and readers complain of poor print quality. (They look like photocopies of just the early chapters of longer editions, and some reviewers say that the most interesting parts of the original are omitted.) Unfortunately, this is such a classic that second-hand early editions are difficult to find and retail for good prices. A PDF of an early edition (images of pages) is available at The Internet Archive. (Since this is about 1000 pages long, you may still prefer to find a modern abridgment.)

This is a classic book dating from 1951 lectures delivered at Harvard by Hermann Weyl. 

Modern printings of this classic are still widely available both new and second hand, but you can download a PDF free from Harvard at Weyl Symmetry.

• The Beauty of Fractals
• The Science of Fractal Images

These books made people aware of the visual impact of fractal images and contain a many striking examples. However, the text requires a certain amount of mathematical sophistication. (You need to understand at least complex numbers in order to follow the algorithms, and though the technical level might not be much beyond A-level, making progress through the book requires a fluency that only comes from practice.)  

There may be more recent books that would do a better job of explaining how you might produce and apply fractals - I just do not happen to own any. (This is likely because fractals are now hugely important in computer imagery.)

The seminal classic "The Fractal Geometry of Nature" by Benoit Mandlebrot from 1982, which originated many of the ideas of fractal analysis is worth a look if you have access to a large library and want to dig into the fundamental ideas. Unfortunately, it is such a classic, and can still be recommended as a good introduction to the concepts of fractals, that secondhand versions command high prices. It is relatively readable for a maths book (at least for those with a modest mathematical fluency) but assumes that you do want to understand the mathematical ideas of fractal geometry. You would not buy it for the illustrations, which reflect the relatively modest computing power then available. 

If you want to apply fractals in advanced and novel ways you probably do need to understand some of the maths, but this is not essential for many imaging applications, because packages of well-written code are readily available. 

My latest purchase is "Indra's Pearls: the visions of Felix Klein" by David Mumford, Caroline Series and David Wright. (Cambridge University Press 2002 and 2015.)

This is a treatment of Mobius transformations showing how iterated transformations can generate interesting fractal images. Although it is an unashamedly mathematical treatment, it covers all the necessary maths in the text at a moderate pace (particularly an introduction to complex numbers) with exercises. It is therefore perhaps not for those with mathematical phobia, but is accessible to anyone who has the inclination but not yet the knowledge.

I have recently been reading "Mathematics and Art - A Cultural History" by Lynn Gamwell. This traces the influence of mathematics on art going back to classical time. A beautiful and highly informative book, substantial in every way (and excellent value if you like to get a lot of weight both physical and intellectual for your money!).

This takes a view of art that you will not find in the convention histories, which are of course probably mainly written by authors who have only elementary understanding of mathematics, given the too common art/science cultural divide in modern education. I was, however, fascinated to discover that the highly influential 20th century "intuitionist" mathematician, Leo Brouwer, chose to live in a commune of artists and architects, and the Bertrand Russel's ideas on formal logic were discussed in the Bloomsbury Group and may have had some influence on artists such as Henry Moore and Barbara Hepworth who wished to develop an abstract language of form.

I was particularly interested in details such as how Leonardo da Vinci got himself instructed in the maths of perspective in exchange for illustrating a geometry book. He used formal perspective in his Last Supper image, which was intended to give the impression of an extension of the room in which it was painted. He then realised, however, that classical linear perspective was not what he wanted in later paintings. The perspective effect really only works properly when the viewer stands in exactly the right position - that used by the artist when constructing the image. If you stand too close to the Last Supper, the figures on the edges appear too small (because they are relatively further away). If you stand too far away you loose the sense of depth. He clearly understood the maths at a level that allowed him to go beyond the simple rules that others used without understanding.