I have referred fondly to Richard Williams' book The Animator's Survival Kit, published in 2001, and I even believe I may take credit for a small bit of it.

Years ago, a friend and I attended the first ever of Richard Williams' Animation Master Class workshops. This was held in Vancouver, BC, November 9, 10 and 11 of 1995. These classes were the basis for the book, or helped work out the ideas to be included in the book;  I am not sure which.  But he was already calling his class "the Animator's Survival Kit" at this time.

It was perhaps on the second day, when we had been talking about animating walks.  There was a bathroom break, and I walked up to Dick and said, "If you are animating a walk cycle, should you animate the character in one place on the page, as for use with a scrolling background?  Or should you walk him across the page?"

Most of what I knew about animation I had learned from books, and from studying animated films directly, so for years I had done walk cycles with the character holding his place on the page and his feet slipping backward, as if I were standing alongside a treadmill where the character was walking.

How walks are often displayed in books on animation. From "Animation in Twelve Hard Lessons", by Robert B. Heath.

Another example, this time by Preston Blair in his well-known book. From "Animation", by Preston Blair, published by Walter T. Foster.

This is how they were usually portrayed in animation books, often with registration marks over each image, so that they could all be lined up, one perfectly superimposed over the next. In some ways this was easier to do, with the body and head just bobbing up and down.  In fact, for a long time I don't believe it occurred to me to do it otherwise. But recently I had realized that perhaps you could get a better feel for the forward movement by letting the character actually step forward across the page, and so I had posed this question to Richard Williams.

There was a pause of several seconds before he answered decisively, "Walk him across the page."

That's all I can tell you about his thought process, or whether or not he had already intended to say something about this. But I can tell you that when the book was published, there it was, on page 111: "...in doing these walks--take a few steps across the page or screen--don't try to work out a cycle walking in place with the feet sliding back, etc." 

Here is a copy of the actual entry:

From page 111 of "The Animator's Survival Kit", by Richard Williams, published by Faber and Faber, 2001.

But more important than whether I was an influence on Richard Williams is the fact that he is right: walking the character across the page is the best way to get the movement right. The other might sometimes work, but it can also look as phony as running in place does compared to actually running over a distance, and getting the feel of the mass and weight moving forward will help you achieve a convincing walk (or run, or sneak or other gait.)

The walk cycle, drawn spread out across the page.

And here's something of my own I want to add: it is important in doing any walk cycle in this way to create a copy of drawing 1 at the end, so that you have a drawing to link into.  Thus if you have a 16 drawing walk cycle, create also a drawing 17 which is a tracing of drawing 1 except that it will be positioned at the end of the second step, where the cycle repeats. This will be a working drawing and never to be photographed, but I think you will find it indispensable.

With a copy of drawing 1 in the new position, you will have something to animate into.