Chemical clocks on the basis of rotating waves. Measuring irrational numbers from period ratios

An ink-jet printer is utilized to generate catalyst-loaded patterns such as circles, triangles, and squares on polysulphone membranes. These patterns define excitable domains for the Belousov-Zhabotinsky reaction in which rotating waves can be initiated. The resulting wave propagation is exploited for the implementation of chemical clocks with stable period ratios. Based on this approach the irrational numbers π, √2, and the golden mean are measured with a relative error of 0.1−0.2%.