I’ve written before about the illusionistic 3-D sidewalk “paintings” in chalk by artists like Kurt Wenner and Julian Beever, as well as the large scale illusionistic murals by Eric Grohe.

Web Urbanist has posted a nice overview, Amazing 3D Art from the Best Street Artists, with a selection of work by Wenner (image above), Beever, and others; including Edgar Muller and Manfred Stader, Tracy Lee Stum, Eduardo Relero, Rod Tryon and Anthony Cappetto, giving you a quick look at some highlights of this apparently growing phenomenon. It also features muralists like Grohe and Greg Brown, and even a 3-D graffiti artist known as Diam.

Some of the pavement chalk art takes the form of large scale reproductions of famous works by artists like Da Vinci, Vermeer, Rembrandt and others.

Much of the work that has made this a phenomenon is based on anamorphoses, images that are distorted in such a way that they only look “right” form a certain vantage point. The limitation is a trade off for the illusionistic power the images can have to appear three dimensional when seen from that viewpoint. You can see an example of how this works here.

Anamorphosis has been used in art for centuries; you can see a particularly striking example of it in Hans Holbien the Younger’s famous double portrait The Ambassadors, which contains the anamorphic apparition of a skull.

The new urban sidewalk artists have used this approach to create images of objects and environments that, when viewed from the correct vantage point, appear to extend above or below the pavement on which they are painted.

Wenner has gotten new, upscale website since I wrote about him, casting himself as available for corporate commissions and highlighting his architectural designs. Beever is still coasting along like a street artist, with a homemade looking, 90’s style site, but he has added additional images.

Wenner’s site includes some videos of him working, and there are some others on YouTube of a short documentary, Masterpieces in Chalk.

If you look around, you’ll find a few not covered in the Urbanist article, like Cuong Nguyen.

Muralists like Grohe or Brown are in the long artistic tradition of “trompe l’oeil” (French for “trick the eye”), in which artists have created images that appear to have dimensionality beyond the surface on which they are painted, relying less on anamorphosis and more on realism. This tradition includes some of the fantastic dome paintings in which the vault of heaven, filled with angels and religious figures floating in apparent disregard for gravity, is projected on the interior of a dome.

Of course, if you step back and think about it, the modernists were right; all representational art is an illusion.

It’s been the subject of much discussion, some suggesting that it is misleading enough that it should be rethought entirely, but the color wheel remains the most common and convenient method for visually understanding and comparing the relationships of different hues.

As part of the Gutenberg-e project by the American Historical Association and Columbia University Press, Sarah Lowengard has written a scholarly treatise on The Creation of Color in Eighteenth-Century Europe, the third chapter of which, Number Order, Form, delves into the history of color wheels and other visual systems of ordering and visualizing the relationships of colors.

The link going around the web currently (I found it on Digg) is to a post on the Color Lovers blog, which has extracted selections from her paper into an article on the History of the Color Wheel.

Color circles have been used to describe associations of colors from medieval times, but the first known example of the representation of hue in the form of a wheel, or circle, commonly suggested as the original color wheel, is traced to Sir Isaac Newton; whose keen mind was for some time focused on the nature of light and color.

Other systematic visual arrangements of colors precede it, like Tobias Mayer’s Trhchromatic Graph [correction - see below], which he first described in 1758 (interpreted by Georg Christoph Lichtenberg, image above, top left), but Newton’s circle is recognizable as the predecessor of the one in modern art texts. (For a couple of color wheels that I find particularly useful, see my links to Bruce MacEvoy’s artist pigment color wheels on handprint at the end of this article.)

Newton’s experimentation splitting sunlight with a prism is relatively well-known. (It’s still a fun and instructive practice is you haven’t indulged in it, I got mine from Edmund Scientific.)

Less well known is Newton’s original color circle, or hue circle, which was actually a kind of pie-chart (image above, top right), in which the bands of color he observed were distributed in wedges corresponding to their width in the observed spectrum, and arranged around the circle in the order of their wavelength. Newton emphasized that his circle represented the properties of the color of light (additive color), not artists’ pigments (subtractive color).

It was Newton who accomplished something that I have long been fascinated with, and confused by — the “closing of the circle”.

Physical wavelengths of light, which our eyes and brains interpret as different hues, can be thought of a part of a linear arrangement, segments of the electromagnetic spectrum; a continuous band of wavelengths of energy from the very short (X-rays and Gamma rays), with wavelengths measured in the distances equivalent to atomic nuclei, to the very long (radio waves) with wavelengths measured in distances on a human scale (meters or 10’s of meters).

The spectrum of visible light sits somewhere in between, at wavelengths the size of protozoa (micrometers, or millionths of a meter, also known as microns), ranging from red on the short end at 700nm, to violet on the long end at 400nm.

But how, my fevered little brain would like to know, does this linear relationship bend back on itself, like the optical equivalent of a Möebius strip, and connect in a continuous band; and how does it fit into that neat and oh-so-convenient system of primary, secondary and tertiary colors, triads; and in particular, the dramatic, and apparently biologically founded, relationship of color wheel opposites, or complementary colors?

This seems to have something to do with a “gap” in the color wheel, between the physical wavelengths of red and violet, in which the purples fill in with colors that are not discrete frequencies on the spectrum, but combinations of others.

I have to admit that I’m still basically unclear about this, but let’s face it, we always knew purple was weird.

Correction and addendum: Divid Briggs, author of The Dimensions of Color, was kind enough to write a comment and point out that though many systems of color charts precede Newton, Mayer’s was not one of them.

He also appears to have an answer to my question about the “closing of the circle”, which comes from the opponent model of vision. He explains if briefly in his comment on this post, and in more detail on The Dimensions of Color.

It turns out that I’m obliquely familiar with this model of human vision, which is based on two “channels” or scales of color, redness vs greenness and yellowness vs blueness, and a lightness scale or channel, in that this is the color model on which the LAB (CIELAB) color space is modeled.

CIELAB (”LAB color”) is a color space used in Photoshop, and is the fundamental color space on which Photoshop bases its interpretations of other color spaces. If you convert between CMYK and RGB, for example, Photoshop converts to the first color space to LAB and then from LAB to the other. (Here’s Adobe’s Technote.)

The CIELAB color space, based in part on Munsell but founded on the biological way in which the cones in the eye react to color, was codified in 1931 by the Commission Internationale d’Eclairage (International Commission on Illumination) to describe all colors visible to the human eye.

The closed circle of the color wheel is a product of the related opponent model of vision in which the interaction of the redness to greenness and blueness to yellowness scales forms a circle, and the oppositions produce the famous complementary color effects with which artists are so familiar.

So there’s my answer. It’s in the eye of the beholder.

Here are a couple of interesting diversions that dramatically illustrate the degree to which color perception is controlled by the effect of previous or adjacent colors.

The first, Big Spanish Castle, is a simple, but dramatic and fun, color-based optical illusion. Based on the visual effects of complementary colors and the optical/brain phenomenon known as an afterimage, the illusion is similar to others in which these principles are used, as in the American Flag illusion on the Wikipedia page for afterimage.

In this case, however, the effect has been cleverly combined with a photograph for a fun and striking effect.

Go to the page linked here, and below, which is posted by graphic designer John Sadowski. There you will find a larger version of the image at top-left. Stare at the dot in the center of the image for 30 seconds (the one on the linked page, not the one here) and then, without moving your eyes, mouse over the image; and you will see what appears to be a color photograph. Once you move your eyes, however, you will find that the photograph is, in fact, black and white. Fascinating.

Sadowski gives links to instructions for creating your own version of the illusion (requires Photoshop), and a list of various versions of the illusion that people have sent in.

The second, which is one of three color perception demonstrations on e-Chalk (image at left, bottom), is one of the most dramatic examples I have seen of how adjacent colors affect the perception of the value and hue of a color.

Choose the “illusion 1″ button at the bottom of the page. The interface requires Flash (which you probably have) and allows you to move a dragable mask over the image, isolating two parts of it that look initially to be radically different colors, dark blue-gray and bright yellow, but are demonstrated to actually be the same color. The effect is quite dramatic. The other two experiments are similar in nature.

There is also a related image on the Wikipedia page for optical illusions that demonstrates the same principle, but with the value of a gray tone. It requires a bit more work on your part to view the proof but the effect is also striking.

All of them demonstrate that color, like beauty, is in the eye of the beholder.

As much as I despise the deliberate campaign by mid-20th Century modernist art critics like Clement Greenberg and Harold Rosenberg to denigrate the history and traditions of western art in order to elevate their own pompous theories (in the process killing realism for half a century), I will grant that they were correct about one thing.

Representational art is an illusion.

It is the illusion of a three dimensional scene or object created by the arrangement of paint or other marks on a two dimensional surface.

With that in mind, most artists should at least have a passing interest in vision, optics and the fascinating subject of optical illusions. (Proponents of the modernist doctrine of flatness are, of course, excused and may go sit in the hall for the duration.)

I’ve featured some optical illusions in the past, such as the calculated space-altering architectural patterns of Felice Varini (images at left, top), the anamorphosis in Hans Holbein the Younger’s The Ambassadors and the anamorphic sidewalk art of Kurt Wenner (left, middle) and Julian Beever (left, two bottom images).

Here are some general interest optical illusions blogs and sites of varying quality and subject matter. They are at the very least fun to poke around in, and at best can be genuinely illuminating.

Of particular interest to artists should be optical illusions that deal with color and dramatically demonstrate how utterly and completely the perception of color is affected by the surrounding colors.

Notable in that respect is this series of color perception experiments on eChalk, which are the most striking examples of that principle I have ever seen.

Benoit Mandelbrot is not an artist in the usual sense of the word. He doesn’t work with oils, watercolors, pastels or colored pencils, yet he has created work of extraordinary beauty.

Benoit Mandelbrot is a mathematician. He coined the term “fractal” in 1975 to describe a shape that appears similar at all levels of magnification. Fractals occur in nature. Go to Google Maps and look at the satellite photo of a large river, then zoom in on the branches of the river, then the creeks feeding those branches, and the runs feeding the creeks. The branching and convoluted shapes of the shorelines remain similar at every level. Similarly, look a a naked tree in the winter and see the relationship of large branches to smaller and smaller branches.

The nature of cloud formations, seemingly too complex for traditional geometry and mathematics to describe, is revealed to be an expression of fractal geometry. (I played with this idea in this page from my webcomic several years ago, in which the background includes “clouds” made from a fractal image, and explained the process here.)

Mandelbrot worked with this branch of math and in the process created one of those wonderfully simple and elegant mathematical expressions, like Einstein’s “E=Mc2″, that is incredibly far reaching. “Beauty” and “elegance” are terms used in mathematics to describe particularly simple yet powerful equations or expressions. Mathematical beauty can create in human beings a feeling of fascination, satisfaction and “rightness” similar to the perception of visual or musical beauty. One of the simplest expressions of Mandelbrot’s “set” is: Z = z² +c, in which the equals sign would actually have small arrows top and bottom pointing in opposite directions.

The arrows on the equal sign indicate that the equation can be processed in either direction, and the result of one operation can become the start of the next, ad infinitum, in a process known as iteration. This process generates 2 numbers, changing over time, that can be used to plot a position on a surface, like map coordinates. If you let the process iterate and assign colors to the way the points change, you can generate an image of the Mandelbrot set (image below, top). Zoom in on that image and you descend into beautiful infinity.

The border of the Mandelbrot shape is a fractal; not only does it posses an infinity of detail as it is magnified, its length is infinite. The fractal geometry along the border of the set displays fantastic intricate patterns, and if you continue to zoom in on the image, you find endless variations of pattern and color. The image above is from Wikipedia and was generated by David R. Ingram, (high resolution version here).

Of particular fascination is the fact that as you zoom into a Mandelbrot image you will find familiar patterns, particularly smaller versions of the somewhat heart-shaped black center of the Mandlebrot itself, that repeat at various levels. (image below, left, also from Wikipedia).

If you zoom in far enough on the edges of those mini-Mandelbrots, you will encounter a subset of smaller Mandelbrots. Zoom in on those and you will find even smaller repetitions of the set. In the mathematical cosmos of the Mandelbrot set, this goes on forever in a mind-boggling infinite “Russian nesting doll” relationship.

PBS has been running a fascinating documentary on this subject, Colors of Infinity, narrated by Arthur C. Clarke (book version here). There are also many resources on the web. Some describe the process, some are about Mandelbrot himself, some are beautiful galleries of fractal and Mandelbrot set generated images, and some are small Java applets that let you generate your own fractal and Mandelbrot images.

Many of the patterns generated by these astonishingly simple mathematical operations are hauntingly familiar. Look through a few fractal art galleries and then think of oriental rugs, Persian decorative patterns, Indian mandalas and paisleys and other patterns familiar in psychedelic art.

This raises some always fascinating questions about the nature of art and beauty. Could it be that we are hard-wired to the universe, our brains genetically tapped into Jung’s images of the “collective unconscious”, and are those hard wired images indicative of the fractal nature of the physical world? Benoit Mandelbrot has given us a beautiful clue.

handprint is the personal site of Bruce MacEvoy. The home page displays an unlabeled group of eight graphic symbols reflecting entry points to the sections of the site, which are a rather bizarre amalgam of his personal interests, from literary experiments to essays on Shakespeare’s Sonnets, human evolution and the philosopher Ludwig Wittgenstein.

One of the symbols is a simplified representation color wheel. Beneath this lies one of the most comprehensive and extensive painting resource sites on the web.

Starting with a guide to watercolor papers, moving on through brushes and paints. In each case the subjects are broken down into sub-sections dealing with history, manufacture, and the details of how to choose between the bewildering array of brands, styles and degrees of quality.

He then goes into selecting palettes, from simple to advanced arrays of colors, and detailed sections on color mixing, color theory and the use of various kinds of color wheels, including a nice one in which painters’ colors are arrayed on a color wheel so you can tell where, for example, venetian red sits relative to burnt sienna in terms of hue and intensity. (There is a larger, downloadable PDF version of this color wheel.)

There is even an extensive section on vision, optics and color perception. His section on techniques not only includes watercolor specific techniques like laying a wash and preparing watercolor papers, but other skills like basic perspective and modeling forms with value and color. Some sections, techniques in particular, are still under development as indicated by names of future topics that are not currently linked.

There is also a section on books, once again extensive, in which MacEvoy reviews and recommends titles on a variety of topics, from learning the basics to advanced color theory. In addition he lists and reviews major art retailers.

Ths site also contains some examples of MacEvoy’s own recent work, which is anything but showcased, you actually have to dig a bit to find it. His style seems as inquisitively eclectic as the topics on the home page of the handprint site, and features some figure painting, portraits and plein air landscapes that are very appealing.

MacEvoy has also posted a journal of thoughts and observations on painting that would make a web site in itself, as would many of the sections and sub-sections of this surprisingly deep site.

As if all of this weren’t enough, under the modest link “artists” is a wonderful section of illustrated essays on dozens of watercolor artists, from botanical and topographical illustrators to greats like Constable, Eakins, Homer and Sargent. Wow.

The site is an amazing resource, unfortunately marred by a less than ideal navigation system and his bizarre decision (what was he thinking?!) to center his columns of text, rendering them unnecessarily difficult to read. (Fortunately this practice isn’t carried to all pages, but it’s prevalent enough to be annoying.)

Don’t let that give you a moment’s pause, though. Anyone with any interest at all in watercolor, color theory, color mixing, vision, artist materials and techniques should check out the watercolors and watercolor painting section of handprint.

Many artists of note have “stand-out” works - paintings, drawings or other works that rise to the top of their oeuvre and serve as the work associated with their name. Hans Holbein the Younger’s The Ambassadors not only fits that distinction, but stands out as one of the most enigmatic and unusual paintings in the history of art.

As I pointed out in my recent post on Holbein, The Ambassadors, the full title of which is actually Allegorical Portrait of Jean de Dinteville and Georges de Selve, is a painting worthy of discussion all on its own.

It is joint portrait, in itself unusual, most portraits are either a single individual or a group. Is presents two highborn French men, Jean de Dinteville (left), ambassador to England and Georges de Selve, Bishop of Lavur and ambassador to the Venetian Empire and the Holy See. The two were friends and are shown with a complex still life of objects in some ways related to their pursuits, a globe, an astrolabe, a sextant, a lute (with a broken string) and a math book, among others. All of them undoubtedly have their allegorical meaning within the context of Holbein’s intention for the image, but exactly what that intention is remains a matter of debate.

The most interesting object in the painting, however, is an elongated, indistinct object that seems to float in the foreground, just above the floor and in front of the subjects of the double portrait. When seen from a certain angle it becomes clear that this is an anamorphic image of a human skull.

An anamorphosis is an image that is distorted in such a way that it only assumes the proportions of a recognizable image when viewed from a certain angle, or by reflection in a curved surface.

Anamorphic images have a long history in art and have been in the public eye in recent years because of their use in the startling sidewalk art of Julian Beever and Kurt Wenner.

The image of the skull in The Ambassadors is only visible as a skull when viewed from below and to one side of the painting. It has been suggested that it was meant to be displayed above a staircase, so that those climbing the stairs would be startled by the apparition of the skull as they glanced upward at the painting. You can see a photographic restoration of the skull image as seen from that angle here.

The painting has been the subject of much speculation, both for the anamorphic skull and the meaning of the various objects arrayed behind and in the hands of the subjects. There are interesting essays here, here and here. There is a list of links on the site of the Department of Mathematics of the National University of Singapore and a short essay on the skull, and other features of the painting on the site of The National Gallery in London, which is where the painting resides.

There are even books devoted entirely to the painting, like Holbein’s “Ambassadors”: Making and Meaning (National Gallery London Publications) by Susan Foister, Ashok Roy, Martin Wyld (additional info here), and Holbein’s “Ambassadors,”: The picture and the men by Mary F. S Hervey.

There in no mention of the painting in Holbein’s extensive records of his major works, yet it is his largest work and the only painting he signed and dated (1533). It was apparently lost from view for for most of the years since it was created until it was “re-dscovererd” by an art historian in the late 19th century.

Symbolic, enigmatic, and masterfully painted, Holbein’s The Ambassadors is certainly a “stand-out” work.

Here is an interesting bit of scientific/artistic conjecture. Christopher W. Tyler, of the Smith-Kettlewell Eye Research Institute in San Francisco suggests in this short (1 page) illustrated article that a high percentage of portrait paintings are arranged so that one eye, presumably the dominant one, falls on the horizontal center line of the image, even when the head appears to be centered in the painting. (He goes into more detail in a second article.)

He cites a number of examples and invites speculation on the part of the reader as to the purposeful placement of eyes in portraits according to several artistic models. His results from a sampling of 282 different artists suggest that he is correct a large percentage of the time and my own casual observations seem to agree.

Get out your ruler and art books and see for yourself.

The site is part of the Smith-Kettlewell Brain Imaging Center, which also includes The Eye Page, with interesting tidbits about eyes, both human and those of other animals, and a series of Art Investigations, scientific inquires into various aspects of art.

Here’s a question for those of you who draw from life: How often and how long do you look at your subject when drawing?

Do you look up at the model or scene frequently, grabbing a fresh impression for each tiny bit of drawing, or do you take in as much as you can in a long hard look, trying to impress a good bit of what’s in front of you on your memory before working on the drawing for several minutes?

Chances are that you glance at the subject frequently, as I do, particularly if you’re tying to be faithful to nature rather than just taking hints from reality with which to be expressive.

Occasionally, I’ve tried to draw a scene or subject from memory (as opposed to making up something from my imagination). I’ve found my ability to do this limited, but our brains may be capable of much more than we give them credit for. People talk about this in the areas of science and mathematics, but it’s relevant in drawing as much as in other areas.

Sometimes people with unusual abilities will make us look at our assumptions about what is or isn’t possible in a new light. Stephen Wiltshire is a autistic savant with a seemingly innate skill for drawing. For background, see my previous post on him.

In the past few years Wiltshire has done a few public demonstrations of his astonishing ability to draw images in detail from memory. In May of 2005 he was in Tokyo. After a half-hour helicopter tour and some additional time viewing the city’s skyline form the roof of a skyscraper (top-left), Wiltshire spent seven days drawing a 10 meter (30 ft.) panorama of Tokyo on the inside of a 360 degree curved surface, without the aid of reference or sketched notes.

You can view a video of the process on the site, from which the screen captures at left are taken. (I apologize for the terrible image quality, but they only offer the videos in Windows Media and Real Media formats, no MPEG or Quicktime. C’mon, people, get a clue.)

There are also similar but less dramatic videos from demonstrations in other cities in the Television section of Wiltshire’s site, in which he demonstrates a similar reliable ability to retain and draw large amounts of visual information with great detail.

I’ve long felt that there is a particular state of mind involved when drawing, in which we see things differently. (See my post on Drawing on the Right Side of the Brain.) When I was young, I used to think of it as looking at things with my “regular eyes” or my “artist eyes”. Some of you may have experienced it as something similar. How many of us have explored the possibilities of expanding on that state of mind, culturing and developing it, in addition to working on our drawing technique?

Savants often express abilities beyond what is considered normal, but how much of what is considered “normal” is the result of assumed or acculturated limitations? At the very least, the abilities of someone like Stephen Wiltshire should give us a hint that we may all be able to train ourselves to see just a little bit more when we’re drawing, or even when we’re just walking down the street.

Felice Varini is an artist who paints on or in architectural elements in a way that creates the illusion of a flat pattern or object where one does not actually exist.

The illusion is visible only from one specific angle; when viewed from other points, you can see the fascinating series of markings that make up the piece. He paints on the outside of buildings, inside of rooms, in corridors, across walls, skylights, doors and archways, often creating the illusion of a physical object in space in the middle of an open area. His patterns are frequently optical patterns themselves, creating a sensation of Op Art by way of Christo.

At first it looks as if the pattern might be Photoshopped onto the image until you see the views from other perspectives; then the remarkable finesse with which Varini has created his patterned spaces becomes apparent. This work in particular is remarkable for it’s scale (not quite Christo scale, but pretty amazing nonetheless) in which he creates his illusory pattern across the space of a city street using painted markings on multiple buildings.

I learned about this from the gravestmor blog, which has a brief overview with a few sets of images. The Felice Varini site itself is harder to navigate, but worth the trouble. See my “Site Quirks” notes below.

Link via gravestmor.