Superstructure - Fly your ship through an equation? Really?

What would you say to the concept of a game where the player is surrounded by landscape created from 3 dimensional mathematical equations? As you fly through such a world, you're really flying through the 3D graphical representation of equations. These equations come to life and morph into other landscpaes in real time, once certain objectives are reached. Sounds too weird for a video game? Perhaps it is, but such a game was made, and has been played by thousands of people. You may want to take a look at it before proceeding to read the rest of this article, so that you may better understand references to it. Download Superstructure by clicking here.

So how would such a game look, you may ask. Well, it will have many faces, since different equations will generate different contours. Still, there are certain familiar charateristics that remain constant. While there are canyons, peaks, and flat surfaces that span the playing field, you will not find caves, or "holes" within the landscape. This is, of course, due to the fact the the equations are all 3 variable functions of the form z=f(x,y). This means that for every (x,y) coordinate, there is exactly one point, which is represented by a block in the game. Take a look at the images below to get an idea of what such a function can look like:

In the first image the player is flying on top of the equation's surface, while in the second image (s)he is flying on the bottom surface of the same equation, though a different part of the equation. Each block you see is actually a point on the equation. Up and down is the Z axis, while the X,Y plane is parallel to the top and bottom surfaces of each block. If you have ever plotted an equation of form z=f(x,y) on a graphing calculator, or using a software on a computer, you may notice the resemblance of these plots to the above images.

When the player accomplishes part of the objectives of the level, the blocks will move up and down creating a very nice effect of morphing. This morphing of the blocks in the +z, and -z directions is accomplished by altering some parameters of the equation. While these parameters are constant, the landscape does not morph. Altering these parameters in real time causes the aperent movement of the blocks in the z direction.

So how does this game accomplish what MOST games do not: THE ULTIMATE IN REPLAYABILITY! Well, first off let me clarify what I mean by that. Each level looks different each time you play. So level one, though will exhibit the same trends, will look different every time you play. Level 2 will exhibit different trends from level one, and will also look different each time you play. Once you get up to higher levels, things will really start to look unexpected. This is accomplished by several scenerios. To make level one look slightly different each time, the same equation is allways used for level one, but with some dynamic parameters randomly generated. This will alter the equation enough each time you play, so that the level will look somewhat different. Up to a certain level, each level has it's own equation. So that explains why there's a big change of trend between levels. After a certain level is reached in the game, several separate equations are calculated with random parameters, and are then combined randomly! This creates a fuction that is the sum of several other functions (becoming one large function), creating some very unpredictable landscapes.

So now you know why this game is so unique. Some other notable aspects of the game are the randomly generated space scenes complete with 3d placed nebulas, and fractal textured planets. This results in a unique space scene every time you play any level. This too will contribute the the ultimate in replayability.

What is the point of making such a game? Well, besides adding yet another game to the vast number of games out there, it was an experiment. This game is the 2nd such experiment I have done in creating a world made purely of equations. The worlds of Superstructure are extreamly simple, but why not create worlds infinitely more complex? To populate a universe of galaxies, filled with worlds to explore using equations is the ultimate video game. Wouldn't it be nice to have a single equation stuff=f(x,y,z) in which the stuff you'd put in any specific x,y,z coordinate would be a function of the equation? How about an even more advanced equation where stuff=f(x,y,z,t), where with the passage of time, stuff would change, perhaps evolve? Well, we all have our dreams, don't we? ;)

Now when you play "Superstructure", you can think of equations of form z=f(x,y) to enhance your experinece.... or not. Above all, have fun, life is too short not too!