Can you predict where iterative math goes just from its start?

When iterative algorithms run on matrices, their early behavior hints at where they'll end up, but comparing short trajectory segments is hard. This work converts the first few steps of iterated Pearson correlations into eight compact fuzzy descriptors capturing contraction speed and evolution. On 22,000 synthetic trajectories, this representation predicts convergence length with R² = 0.648, nearly matching raw trajectory data while being interpretable and compact.