Brainfilling Curves: The Root 16 Triangle Grid Family

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The Root 16 Triangle Grid Family
A chapter from Brainfilling Curves by Jeffrey Ventrella

1 Horror Vacui 2 A Very Patient Turtle Who Draws Lines 3 A Taxonomy of Fractology 4 Gallery of Specimens

Root 2 Family

Root 3 Family

Root 4 Square Grid Family

Root 4 Triangle Grid Family

Root 5 Family

No Root 6!

Root 7 Family

Root 8 Family

Root 9 Square Grid Family

Root 9 Triangle Grid Family

Root 10 Family

Root 12 Family

Root 13 Square Grid Family

Root 13 Triangle Grid Family

Root 16 Square Grid Family

Root 16 Triangle Grid Family

Root 17 and Beyond...

5 My Brain Fillith Over

6 References

7 Acknowledgements

Like the root16 square grid family, the root16 triangle grid family has many spacefilling curves that pertile equilateral polygons - in this case, triangles. I would like to show you a few. None of these examples are self-avoiders...but when rendered with rounded corners, they reveal some unique characteristics. The next four specimens each have a segment of length 2 that lies horizontally across the middle of the 4x4 triangle that houses the generator. This horizontal segment is responsible for extending the curve upward towards the pinnacle - increasingly with each fractal level.

On the next three pages are triangular specimens that I have rendered in color. The last one has the top one-fourth of the triangle rotated 180 degrees and enlarged, to its right.

Here are some non-triangle specimens with three-way symmetry. These tightly-coiled curves are of the dense variety that evade being pulled apart to breathe by way of rounded corners. But they do have interesting chambers. The second specimen is rendered with its various chambers colored in a playful manner.