Shades of summer, seen from 250 miles up. 🌊 From the International @Space_Station, Earth’s blues stretch across coastlines, oceans, and islands in a way only astronauts get to see — a shifting palette shaped by sunlight, atmosphere, and the motion of our planet below. Will you be exploring any beaches or waters this summer?

Shade the even entries in Pascal’s Triangle (just mod 2) and the Sierpinski Triangle literally emerges from simple addition. This is Lucas’s Theorem unfolding the hidden recursive symmetry buried inside binomial coefficients. > Binary Logic: C(n,k) is odd only if every 1-bit in k’s binary is also a 1-bit in n’s. > Fractal Convergence: Density of odd entries → 0 as rows grow, forming the classic Sierpinski gasket with Hausdorff dimension ≈1.585. > Emergent Complexity: Pure discrete combinatorics spontaneously births continuous fractal topology.