*updated 7/10*

The following is an interesting example of Temporal Aliasing I discovered while working in 3d software.

A large grid seen rotating at a certain speed will appear to group itself into smaller grids, spinning independently.

In this example, we see a central grid, and 3 or 4 orbiting it. To prove it’s one grid, stand back from your monitor.

The illusion/effect has been picked apart by several sources, some intelligent professors and many more angry students have contacted me about it. MIT‘s Fredo Durand gives probably the easiest to understand explaination:

You are trying to capture a motion that is too fast for the framerate you’re using. In the case of a spinning wheel, what happens is that the wheel might turn, for example, 350 degrees between two frames but your eyes interpret it as -10 degrees. A similar thing happens with your grid. At the periphery, the lines move by more than one grid cell between two frames and the resulting visible motion is “snapped” to the smallest possible motion. The correct way to prevent such artifacts is to make sure that the shutter of the camera is open during the full interval between two frames, so that motion that is too fast gets blurred.

Further detail by Professor Berthold Horn (also from MIT):

“Perhaps an illustration of how we seem to interpret rotational
motion as taking place about points near the center of the field of view,
if possible, or so it seems to me. As I move my gaze around,
I tend to pick up apparent rotations about points near the center
of the current view (where temporal aliasing permits).

Reminds me of an apparent higher ability to detect symmetries in
patterns when the axis of symmetry passes near the center
of the field of view, or the center of symmetry is near the center of
the field of view.

Could it be that circuitry for detecting symmetries is expensive and
would need to be replicated for different centers of symmetry?
Which might suggest that there is good circuitry for “central” symmetries.
Others are found or at least verified by shifting the gaze…
Perhaps something similar applies to rotational motion.  Although,
we’re very good at picking up rotational motion from peripheral vision…”

Mathematician Cristi Stoica made this amazing one which has 2 centres.

and this, which has 4 centres…

he writes:

If we rotate the grid at each step with an angle of 360/n, the center is the only point containing all the time vertices of the grid (except, of course, the case when n=1, 2 or 4, when no rotation is viewed). But if we are good enough at math, we can modify the animation such that we obtain more than one fixed point….

The animation above is based on some properties of the number 65. This number plays the role of the hypotenuse in eight Pythagorean triples:
65²=16²+63²=25²+60²=33²+56²=39²+52²=52²+39²=56²+33²=60²+25²=63²+16².

Also:

Interesting discussions at reddit, abc science, bad astronomy

Japanese page with flash applications

Variations made by someone named Theeth (here and here)

seanaltogether created these interactive flash rotating grids: here and here

My original images:

Here there appear to be about 5 or 6 grids.

at a lower frame-rate it looks almost like liquid.

This is a subject which crosses my mind the more I see new animation work coming out. I’d like to share it in the hope its of use to image makers and viewers alike.

Everyone in the business of filmmaking is constantly aware of the rule relating to the Safe area (also called TV cutoff). All design for television is made with an invisible border which clips about 20% of the image. It’s a long established rule that all movement must take place within one border, and all text within another.

This rule is, in my view, completely outdated and unnecessary, and may be officially forgotten about immediately. It simply lacks any practical application considering how most video is viewed today, digitally, online and on modern screens.

As a symbol of where we are now I feel it’s time to drop it and start taking advantage of the full-frame.

From an animation point of view, it’s always been quite vexing to have to keep everything within a certain frame, but still to work to an outer frame just in case.

From a design and composition point of view you want to use your full canvas without restriction, to create a certain balance (or lack of balance) and know your audience will see the same thing. Unfortunately with the Safe Area rule you would have to make a composition work within one frame, then extend it out for posterity. (It must surely be frustrating to anyone involved to have all that old work now be seen exposing the full frame, not what the compositions were designed for.)

This was something I considered when doing my short film Wofl in 2006. The trees in certain shots fit into square shapes, a simple motif which helped establish that world. I can say that, less obviously, they were an expression of frustration at fitting things into this arbitrary frame. They are actually fitting snugly into the Safe Area.

Breaking this rule 5 years ago would be considered unprofessional, but things most certainly have changed, despite this so many still blindly cling to it. For example, a small segment I did for the Boing Boing blog some months ago had images with text that filled the frame. When the thing went online, an editor somewhere had gone in and neatly fitted the image down without thinking. There’s something inexplicably dull and mediocre about the result, small enough as the change seems to be.

The Safe Area is part of a long list of rules which I find useless in modern image making. They reoccur as default, unquestioned laws which will unfortunately paint all which we see as the 00′s style in 10 years.

I really believe we ought to be questioning every rule we are told, especially with animation, when – as trite as this remark will always sound – you can do anything.

David

The splash page of this site now has a showreel, it’s the first time I’ve ever had one online… not normally a fan of these things but it’s a publicity obligation. It should be a good introduction to my work for the uninitiated.

Youtube embed below…

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