Shapes: The basic pattern is three lines spiralling out from a center point. Each line's outer endpoint moves around the screen, bouncing off the edges. Lines will have some amount of history (more on faster devices) fading out behind them. When lines bounce, ripples are created which flow down to the central point.

Sounds: Whenever an endpoint bounces off the edges of the screen, it plays a note based on the color the endpoint was at the time of the bounce.

Interaction: Lines will tend to gravitate towards touch events, with each line following a different event.

Notes: This one was Luka's idea. It took a lot of tuning to get from "there should be a mode with rainbows spiralling out" to this. Early on, the inner parts of each spiral were very smooth, and the outer parts much blockier; the math that corrects for this is why the edges curve out a little right near the end. In an early version, I did a ton of work trying to make the lines spin, calculating them going out; it became a lot easier when I switched to generating points and calculating inwards. This is probably my favorite mode. And yes, the name is a reference to the They Might Be Giants song.

Shapes: There's a grid of hexes of varying colors. There is an active point of each color. These points move around the grid. Each time a point moves, it looks at the three hexes in front of it (they have a facing, which is not displayed), and moves to the one furthest from its own color and full brightness. The hex it moves to is changed to its color and full brightness, and the two squares behind it and on the sides are nudged towards its color and made a little brighter. The whole field slowly fades.

Sounds: There's a background pattern of regular notes. If one of the painting hexes tries to overwrite one of the other hexes, it plays a tone. If you are touching the screen, that will also play tones.

Interaction: If you touch a hex, that hex and the hexes near it are brightened, and the hexes near it are shifted towards its color. If you then drag your finger around, it will continue nudging hexes near your finger towards the color of the hex you first touched. Multiple simultaneous touches work, with each having its own color. Notes are played corresponding to the color of the first hex touched.

Notes: In an early version, the painting hexes went solely by color-difference, ignoring brightness. If you left it for a while, eventually each pair of opposite colors (yellow and purple, red and green, blue and orange) would end up following each other in a small circle. The slight preference for darker squares prevents them from getting stuck.

Shapes: There's a square grid, with six active points on it. The points take turns jumping around in random knight's moves. The square it lands on is advanced in color twice (red through orange to yellow, for instance), and the four adjacent squares are advanced once. The whole field slowly fades.

Sounds: Backdrop of tones, plus knights will play a tone based on the color they have changed a square to.

Interaction: Knights will tend to move towards touch events, with each knight preferring a different finger in multitouch.

Notes: This was the first mode which was really interesting. The combination of knight's moves and plus signs was chosen so that a knight will always adjust things near what it last adjusted, but never any of the squares it hit on its last move.

Shapes: A simple four-point spline curve bounces around the screen. Each of the four control points is bouncing separately.

Sounds: When one of the control points bounces off an edge, a noise is played.

Interaction: Touch events attract the control points, with the first two multitouch events attracting the ends of the line.

Notes: While the source for this was translated to Lua, the original logic for the calculations was written sometime in early 1994, when I wrote this display for the Amiga. It was rainbow-colored then, too.

Shapes: Another field of squares. In this one, successive rows are filled out by a cellular automaton. For each square, if exactly one of the square above it and the square to the left of it are highlighted, the new square will be highlighted. Highlighted squares are drawn about one hue ahead of non-highlighted squares, with each row nudging both hues forward a bit. Highlighted squares are set to full brightness, unhighlighted squares are nudged up a bit; the entire field slowly fades. If a row has no highlighted squares, a random square is highlighted.

Sounds: Sounds are played corresponding to the number of distinct regions in each row.

Interaction: Squares which are touched are flagged, and the next time processing reaches them, it will treat them as having an inverted state. Also, the cascade follows device orientation; the next row is "down", rather than moving in the same direction all the time.

Notes: It only takes one or two squares being out of sync to produce some very interesting patterns, but the essential fractal triangles nature persists.

Shapes: Lissajous figures, with delta changing slowly over time, and some history. Starts with a = 2, b = 3.

Sounds: When one of the six points that correspond to particular colors crosses from positive to negative, a sound is played.

Interaction: Touching the screen adjusts a and b, with a ranging from -2 to +2 or so, and b ranging from 1 to 5 or so. There's also a lot of fancy math to nudge the ratios away from degenerate cases which don't look pretty.

Notes: When I first described the Modus to my mom, she pointed out that my dad used to watch lissajous figures on an oscilloscope for hours. I did too, come to think of it.

Shapes: Raindrops appear, expand while fading, and disappear. At the start of the mode, they appear in rainbow order; however, they have varying durations, and are re-inserted in the list in the order that they disappear, so they can eventually end up pretty shuffled.

Sounds: Each drop has a preferred color and octave, and plays that sound when it appears.

Interaction: Touch events and drag events create chains of points where future drops will spawn.

Notes: This was originally slightly prettier, but it was unbelievably slow on anything but the iPad 3. The raindrop images are pre-rendered, and are just being scaled and faded.

Shapes: This is the same basic design as the other Spiraling Shape pattern. The difference is that the center point is not anchored to the screen, although it tends to move towards the center of the screen.

Sounds: Same as for the original spiraling shape mode.

Interaction: The significant difference is that the first point in a multitouch event attracts the center of the spiral, rather than one of the arms. If there's no touch event for that point, the spiral acts as though you were touching the center of the screen.

Notes: I did this mostly to see what it would look like. I'm not entirely sure whether it's a good idea or not, but it sure is interesting.

Shapes: A field of hexes, much like the ones in Painting Hexes. the difference is that in this one, the points tend to wander in or near the direction they're currently moving and don't react to their scenery.

Sounds: Same behavior as Painting Hexes.

Interaction: Also the same behavior as Painting Hexes

Notes: This was the first hex display mode, and existed mostly to test out the display code. But I sort of like watching it, even though it doesn't do as much.

Shapes: This mode is similar to the Cascade mode, differing primarily in the interaction rules.

Sounds: Same behavior as the Cascade mode.

Interaction: This mode ignores device orientation. However, instead of touched squares being marked for processing the next time the display gets to them, they start cascading immediately, causing lines under them to get recalculated.

Notes: It took something like three hours to get from a perfectly clear description of what I thought I wanted to something which actually did it.

Shapes: A line (or possibly several lines) bounces around the screen, leaving a large amount of history behind it.

Sounds: When the moving points bounce, they play sounds based on the line's current color.

Interaction: Touch events attract points. Multitouch causes additional points to be added, so a three-finger touch will cause a triangle to bounce around the screen. Single touches will cause the additional lines to get dropped.

Notes: This is another mode that I first implemented as a graphics demo on the Amiga in the early 90s.

Shapes: This is, as the name suggests, a variant on Knights. In this mode, rather than advancing colors around the rainbow, the knights set the square they land on to their own color, and migrate nearby squares towards their color.

Sounds: Similar to Knights, but the sound played is based on the color the square had before it got changed, rather than after it got changed.

Interaction: Same as Knights.

Notes: The initial display with diagonal rows of colors is based on the way I had a keyboard painted some years ago.

Shapes: A grid of squares, which range from smaller, dimmer, red squares up through larger, brighter, fuschia squares. This roughly represents a level of energy; brighter squares have more energy, which tends to spread over time. Random locations get energized.

Sounds: Lower tones for the random background energy, higher ones corresponding to the colors of squares that the user interacts with.

Interaction: Touch events add energy, with the amount of energy decaying somewhat over the duration of a touch event, but being increased by the energy of squares touched.

Notes: This is probably the most complicated of the modes, and will not work well (or have many squares) on devices with slower CPUs. The benchmarking for it is a little approximate.

Shapes: Sets of lines bouncing around the display; similar to the Bouncing Lines mode, but there are multiple separate sets, and they are picking points to move towards rather than reflecting off walls normally.

Sounds: Tones reflect the colors lines have when they bounce.

Interaction: Lines slightly prefer to move towards touch events.

Notes: This display is unusual in that it can look much better with un-smoothed lines.

Shapes: Similar to the Fire mode, but there are six points that move around adding energy, similar to the knights in the knights modes.

Sounds: The moving points have their own tones.

Interaction: As with Fire, touches add energy.

Notes: The only real difference from Fire is the more structured energy input.