ML on Apple ][+

Machine learning meets nostalgia as one programmer tackles k-means clustering using APPLESOFT BASIC on an Apple II+. The recursive algorithm, which partitions data points into clusters, achieves 90% accuracy classifying Gaussian-distributed observations on hardware from the late 1970s.

K-means works through elegant simplicity: randomly place cluster centers, assign each data point to its nearest center using Euclidean distance, then recalculate centers based on those assignments. Repeat until convergence.

The implementation required creative workarounds for BASIC's limitations. Since expensive square root calculations weren't necessary for distance comparisons, the programmer used squared distances instead. Memory management became crucial, as redeclaring arrays triggers errors in APPLESOFT BASIC.

Visual elements enhance the demonstration. The program draws decision boundaries between clusters in real-time, showing the algorithm's iterative progress. A perpendicular bisector between cluster centroids creates the classification boundary, with special handling for vertical slopes and screen edge cases.

The project bridges decades of computing evolution. What Stanford's CS229 teaches as introductory unsupervised learning now runs on vintage hardware with 48KB of RAM. Despite the constraints, the fundamental mathematics remain unchanged, proving that core machine learning concepts transcend technological generations.