M.i.P. Trip

The Latin phrase multum in parvo means “much in little”. It’s a good way of describing the construction of fractals, where the application of very simple rules can produce great complexity and beauty. For example, what could be simpler than dividing a square into smaller squares and discarding some of the smaller squares?

Yet repeated applications of divide-and-discard can produce complexity out of even a 2×2 square. Divide a square into four squares, discard one of the squares, then repeat with the smaller squares, like this:

2x2square2


2x2square3


Increase the sides of the square by a little and you increase the number of fractals by a lot. A 3×3 square yields these fractals:

3x3square2


3x3square3


3x3square6


3x3square7


3x3square8


3x3square9


3x3square10


And the 4×4 and 5×5 fractals yield more:
4x4square1


4x4square2



4x4square4


4x4square5


4x4square6


4x4square7


4x4square8


5x5square1


5x5square2


5x5square3


5x5square4


5x5square5


5x5square6


5x5square7


5x5square8


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