Limits of Calligraphy

The concept of Ambiguity of Limits is based on Zeno's Paradox, which states that you can never reach your destination if you keep halving the distance between you and your destination. In this image, a single tile is placed in the center of a picture frame. Around the perimeter of the tile, an algorithm is used to draw a contiguous ring of half-size versions of the tile. This process is repeated eight times, until the tile size is smaller than a pixel. If the algorithm were to run indefinitely, it would never reach the outer edge of the picture frame. This is because the distance between the tile and the edge of the picture frame is constantly being halved, and as the tile size approaches zero, the distance between the tile and the edge of the picture frame approaches infinity.

The central tile in the image consists of an algorithmic stroke. This stroke is similar to a hand-drawn pen stroke in a calligraphic exercise. It is created by joining two randomly chosen adjacent corners of the tile with a crescent-shaped area formed by two Bézier curves.

The Ambiguity of Limits is a fascinating concept that demonstrates the power of mathematics. It shows that even though something may seem impossible, it can still be possible if we use the right tools. In this case, the right tool is mathematics.

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