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Visualizing the Collatz Conjecture: A Shower Thought Turned Stunning

2025-05-20

A scuba diving trip sparked a shower thought that led to a beautiful visualization of the Collatz Conjecture. The author cleverly translates the iterative process of the Collatz function into binary fractions, plotting the results. The resulting graph reveals striking self-similar patterns, almost resembling alien script. Surprisingly, this mirrors a 2019 paper by French mathematician Olivier Rozier, although their construction methods differ. The author's straightforward approach is easy to understand and invites exploration of the graph's hidden patterns.

AI-Powered Crossword Generation: A Breakthrough

2024-12-23

Bill Moorier, a programmer, has been developing computer programs to generate crosswords for years. Recently, incorporating modern AI techniques, he's achieved remarkable results, producing crosswords that rival human-created ones. His approach combines traditional computer science algorithms and modern AI models. It begins with a massive wordlist, refined by AI to remove obscure terms. A grid with 180-degree rotational symmetry is then generated, filled with words using a backtracking search algorithm. Finally, a large language model generates clues, with post-processing to avoid revealing the answers. The system currently generates a complete crossword roughly every two minutes, though imperfections remain, such as occasional clue leakage (especially with acronyms). Future plans include themed crosswords, a significant challenge in crossword generation.