This article explores the problem of short-term earthquake prediction based on spatio-temporal variations of seismicity. Previous approaches to this problem have used precursory seismicity patterns that precede large earthquakes with "intermediate" lead times of years. Examples include increases of earthquake correlation range and increases of seismic activity. Here, we look for a renormalization of these patterns that would reduce the predictive lead time from years to months. We demonstrate a combination of renormalized patterns that preceded within 1-7 months five large (M > or = 6.4) strike-slip earthquakes in southeastern California since 1960. An algorithm for short-term prediction is formulated. The algorithm is self-adapting to the level of seismicity: it can be transferred without readaptation from earthquake to earthquake and from area to area. Exhaustive retrospective tests show that the algorithm is stable to variations of its adjustable elements. This finding encourages further tests in other regions. The final test, as always, should be advance prediction. The suggested algorithm has a simple qualitative interpretation in terms of deformations around a soon-to-break fault: the blocks surrounding that fault began to move as a whole. A more general interpretation comes from the phenomenon of self-similarity since our premonitory patterns retain their predictive power after renormalization to smaller spatial and temporal scales. The suggested algorithm is designed to provide a short-term approximation to an intermediate-term prediction. It remains unclear whether it could be used independently. It seems worthwhile to explore similar renormalizations for other premonitory seismicity patterns.