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Invader Fractal
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The Invader Fractal is a region of space filled recursively with 15 bit combinatoric objects affectionately called Invaders. Look carefully and you might see your childhood experiences with computers unfold in the maze of icons.

CLICK an Invader to destroy it. The empty space will then be refilled with more invaders. This is the strategy of the invaders.

  figure a. a few of my favorites.  
Hundreds and even thousands of Invaders are arranged in this computational construct so that eventually the space is filled completely. The space filling algorithm used here is similar to the one used in the Emotion Fractal.

figure b. the internal bitwise representation of the Invader is only 15 bits, while its graphic appearance is 25 bits.

The Invader itself occupies a 5 x 5 grid of blocks (25 bits). Internally, the Invader is represented by a 3 x 5 grid (15 bits) because it is also horizontally symmetric. The left side of the Invader simple draws identical to the right.

If we iterate through all possible combinations of lighting bits in a 3x5 grid, and eliminate no invaders on the basis of shifted similarity, there are 32,768 (2 to the 15th power) unique Invaders.

figure c. 1,936 unique Invaders, a mere 6% of all possible Invaders.

What is most interesting in this work is the way in which a very small amount of information (15 bits) can be represented graphically, so that it can be more easily remembered by the human observer.

  jtarbell, july 2003  

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