When I first learned that 1/3 = 0.333333..., an endless river of digits, it felt almost mystical. With time, that feeling passed. If anything, repeating decimals felt like an annoyance, nothing more than an invitation to rounding errors. But I recently recaptured that old sense of wonder when I made an artwork from a chart of the repeating parts, or repetends, of different fractions in different bases. Although the original image is meant to stand on its own as a kind of abstract butterfly collection, I kept finding little mathematical easter eggs as I stared at it. I made this interactive version of the chart for fellow recreational mathematicians. Move your mouse over the pies. What patterns can you spot?
