Fractals in nature (think fern fronds, tree branches, river networks) give rise to beautiful patterns. Counterbalancing forces result in lovely complexity, in which positive, accelerating feedback is resisted by negative, stabilizing feedback, enabling dynamic systems to grow, adapt, and flourish. A mix of science, math, and art, the simple and repetitive processes that create natural fractals can also be harnessed by computers — what I do here — to generate mathematical fractals, which are simple to explore and stunning to observe.