I modify here a chapter title from Rodin on Art, which you will love if you read it. Chris cites this book in his question:
You'll have to do another post some time to explain exactly how a canvas can undulate. I remember something in Rodin on Art about evoking motion with the motionless art. But I think that was either physical or psychological motion. Not the monotonous swaying something does when left to the mercies of tender elements, which is what I think of when one says "undulate".
For the sake of argument, I'll consider that a fair definition of undulate. Let's take a look at some key bits of the Rodin text and see if they don't apply to the problem at hand. Rodin speaks to his amanuensis, Paul Gsell, on page 68:
"Note, first, that movement is the transition from one attitude to another.
"This simple statement, which has the air of a truism, is, to tell the truth, the key to the mystery. ...
"It is, in short, a metamorphosis of this kind that the painter or the sculptor effects in giving movement to his personages. He represents the transition from one pose to another - he indicates how insensibly the first glides into the second. In his work we still see a part of what was and we discover a part of what is to be."
Gsell then applies the principle Rodin has just described to Rodin's own sculptures. First he looks at Iron Age, which I'm pretty sure is the sculpture we call Age of Bronze:
I noticed that in the first of these works the movement appears to mount... The legs of the youth, who is not yet fully awake, are still lax and almost vacillating, but as your eye mounts you see the pose become firmer - the ribs rise beneath the skin, the chest expands, the face is lifted towards the sky, and the two arms stretch in an endeavor to throw off their torpor. The subject of this sculpture is exactly that - the passage from somnolence to the vigor of the being ready for action.
Well, you have to have pretty developed taste to figure all that out. His description of his second example, John the Baptist Preaching, proves easier to understand when you look at the sculpture:
In the same way I next studied Saint John. And I saw that the rhythm of this figure led, as Rodin had said, to a sort of evolution between two balances. The figure leaning, at first, all its weight upon the left foot, which presses the ground with all its strength, seems to balance there while the eyes look to the right. You then see all the body bent in that direction, then the right leg advances and the foot takes hold of the ground. At the same time the left shoulder, which is raised, seems to endeavor to bring the weight of the body to this side in order to aid the leg which is behind to come forward. Now, the science of the sculptor has consisted precisely in imposing all these facts upon the spectator in the order in which I have stated them, so that their succession will give the impression of movement.
As you can see, while specific movements are dissected here, the principle is universal: by combining elements of the before, the during, and the after, the artist is able to produce an impression of motion in the work. Let's take a closer look at my undulating cloth:
What's going on here? The same, well, let's call it Gsellian Transition. Because fancy words are cool. What is the transition? Between domination by gravity and domination by wind. The cloth has mass, it should hang down. It is anchored over the arm, and by the hand. All the cloth should droop away from the arm and the hand. Instead, it seems to rise at the bottom, as if a force - an upward gust - were pushing it upward, and it were rippling because it is not a rigid body. But on the right side, it flairs outward as well. This is against gravity, but it is also inconsistent with an upward gust from below. It would only do this in real life if it were starting to be inflated from inside.
In fact, I was thinking of none of that while I was painting it, because I was painting it from the perspective of shape, not physical justification. I was seeking a combination of curves that read naturally to me, but had this strange floating quality. It is this that I called "undulation," and it is common in the sort of Renaissance and Baroque religious paintings I was discussing before. While the eye perceives it in terms of a fairly loosely defined, but internally consistent, set of physical laws, producing a strange wreathe-like movement of the cloth around the figure as if it had its own serpentine intelligence, for me at least, producing the effect is a matter of shape, not of depiction. One must simply evaluate and understand the internal aesthetics of folding in drapery. This reaches a highly advanced state in Art Nouveau, particularly as done by Mucha:
But it has been going on for a long time. This is Botticelli working during the Renaissance:
The cloth in this painting follows an internal cloth-aesthetic, which is never seen in reality except in starched cloth made to billow unnaturally, or in instants when cloth is lifted by wind. I would contend that it is a hold-over from medieval iconography. It does not appear in ancient Greek sculpture, but in the crude representationalism of the medieval period, it does appear. It produces such a majestic effect that, even after the revolution in representation of the Renaissance, it was simply polished up to look more real - and persisted down to the present age because there is something delightful to the eye about unrealistically billowing and undulating cloth.
This is what I'm getting at in my own painting, in my unpracticed and clumsy way. We'll see how good I can get it by the end.
Let me get back to Rodin and Gsell for a second:
"Have you ever attentively examined instantaneous photographs of walking figures?" Rodin suddenly asked me.
Upon my reply in the affirmative, "Well, what did you notice?"
"That they never seem to advance. Generally they seem to rest motionless on one leg or to hop on one foot."
"Exactly! Now, for example, while my Saint John is represented with both feet on the ground, it is probable that an instantaneous photograph from a model making the same movement would show the back foot already raised and carried toward the other. Or else, on the contrary, the front foot would not yet be on the ground if the back leg occupied in the photograph the same position as in my statue.
"Now it is exactly for that reason that this model photographed would present the odd appearance of a man suddenly stricken with paralysis and petrified in his pose...
"And this confirms what I have just explained to you on the subject of movement in art. If, in fact, in instantaneous photographs, the figures, though taken while moving, seem suddenly fixed in mid-air, it is because, all parts of the body being reproduced exactly at the same twentieth or fortieth of a second, there is no progressive development of movement as there is in art."
This is tremendously important for the painter, and Rodin sums it up a little later:
"It is the artist who is truthful and it is photography which lies, for in reality time does not stop, and if the artist succeeds in producing the impression of a movement which takes several moments for accomplishment, his work is certainly much less conventional that the scientific image, where time is abruptly suspended."
Let me avoid endorsing Rodin's judgment of relative truth one way or another, and simply say - this is a fundamentally important difference between painting and photography. Painting carries within it a small extension of time. Photography is very bad at doing this directly - after a few initial 19th century efforts at "painterly photography," photographers gave up on the category entirely. Painting and photography only look the same: painting is pregnant with time in a way that photography is not.
We've covered here muscular motion and the undulating motion of drapery influenced by multiple poorly-defined forces. But the really important category of motion, for me, is the motion of the soul. Because painting can diffuse the time within the painting over several moments, it is possible to capture the soul in a state of transit between what was before, and what will be after.
This is a nearly mystical description, although I'm sure you could reduce it to inconsistent juxtapositions of muscles of the face. This juxtaposition is the physical substrate: the evolution of the soul is the subject. Every time you have a sensation of complexity in a face in a painting, you are responding to an image which contains not an instant, but a moment. Painting can show every subject changing, even the most important one, and this is one of the core means by which it is able to change you.