Visualisers

A visualiser draws a thing rather than running one. Nothing here evolves in time: the thing drawn is the same at every moment, and whatever moves, a camera turning round a molecule or a pen tracing out a Fourier series, is only a way of looking at something already fixed. That is the whole distinction from the simulators, and it is a real one rather than a filing convenience, because it changes what the tool is for. You come to a simulator to find out what happens next, and to a visualiser to understand a shape. Most of the visualisers here are 3D anatomy explorers, and their data source, licence and build are set out on the anatomy hub. Unlike every other visualiser here, they cannot be embedded on another site.

Molecular geometry is the clearest case. VSEPR is a set of rules about where electron pairs sit, and the answer is a shape: trigonal bipyramidal is a fact about angles, not a sequence of events. Reading it off a static diagram in a textbook means holding the third dimension in your head, which is exactly the part people find hard. Turning it around removes that problem.

The graphing calculator and the unit circle explorer sit here for the same reason. Each answers what a relationship looks like, and neither animates anything: the point on the unit circle moves only when you move it, by dragging, with the keys or with its buttons. The Fourier series visualiser does animate, but only the circles and the pen they drive: the sum it draws is settled by the number of terms before the first circle turns.

Why these are not simulators

The line is drawn on something checkable rather than on a feeling. Each of these tools advances at most one thing as time passes, and never the thing it draws: the camera angle on the 3D models, or how far the Fourier series visualiser’s pen has gone along a sum its terms have already fixed. The structure they draw is the same at every moment. A simulator advances state that belongs to the model: a position, a charge, a strip count, a membrane voltage.

That test is worth stating because the categories used to disagree with it. Four of these were filed as simulators, on the strength of having a play button, when all their play button does is spin the view. Calling a static structure a simulation sets an expectation the tool then fails to meet, and someone looking for something to happen concludes it is broken.

Reading a three dimensional structure on a flat screen

Depth on a screen is a guess, so these do not rely on it alone. Bonds and atoms further from you are drawn smaller and dimmer, the geometry is labelled with the angles that define it, and every structure can be turned with a drag or with the arrow keys so you can resolve any ambiguity by moving rather than by squinting.

The numbers are printed alongside for the same reason. A bond angle of 107 degrees on ammonia is the fact worth taking away, and reading it off a rendered picture by eye is not reliable, so it is written down.

Sources, because a drawn structure is still a claim

A rendered molecule looks authoritative in a way a number does not, which is a reason to be careful rather than relaxed about where the geometry comes from. Each of these cites the result it draws: VSEPR after Gillespie and Nyholm in 1957, close packing after Kepler and Barlow, the double helix after Watson and Crick in 1953 with Franklin and Gosling in the same issue, and the Fourier series after Fourier in 1822.

The anatomy explorers draw a dataset rather than a result: every mesh comes from BodyParts3D, © The Database Center for Life Science, segmented from imaging of one adult male body, and the anatomy hub sets out its licence.

The graphing calculator is the exception, and for a good reason: the relationship it draws is whatever you typed, so there is nothing to attribute. What it does instead is refuse to guess. An expression it cannot read produces a message naming the problem, rather than an empty set of axes.