Graphics Gallery

These are mostly animations that have not yet appeared in my tutorials. If they aren't moving, try clicking your browser's refresh/reload button. I made most of the stills with either MathGV or QBasic45 or Paint, and animated them with Snap and MS's Gif Animator.

The level curves of a triply periodic function (of x, y, and t). A topographic map. It repeats in the up-down and the left-right directions, and with time.

A graph of sin(cx) where c varies periodicly. I explain it in one of my trig tutorials.

My 7-year-old and I made this one. The position of the car is a linear function of time, roughly, so the velocity is constant (for a while) and the acceleration is zero..

MathGV can make 3D pics, but I haven't really gotten the hang of making them beautiful.

This is a polar graph, a "16-petal rose", of r = cos(8 theta + time) plus some decoration. It requires only 6 still frames because the period is so small.

This was my very first animation, before I had any idea what I was doing.

Though this may appear 3D, it is a combination of several simple 2D graphs (of parametric equations). For example, the top half of the yellow "diamond" comes from the usual equations for a circle:

x=cos(t) and y=sin(t)

except that I added t/10 to y (to make the "circles" rise) and multiplied x by 10-t (to make them shrink). The "circles" look like ellipses partly because I dilated the screen to get the 3D effect. This animation uses 8 stills.

It is beautiful to watch these fractal images being created one pixel at a time (but I can't show you that!). The graphic on the left is animated (click refresh/reload) to show you an approximation of this. They use a well-known linear algebra algorithm (maps with determinant = 1). In picture 2, I have changed the algorithm so that the color shifts and the shape grows with time. The other two are stills from a similar shrinking algorithm. Notice "the branch is the tree" property.

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Page created 1/21/02.