Calculation of fractal dimension from cattle thermoregulatory responses

Fractal dimension analyses have previously been shown to objectively classify thermoregulatory responses of cattle to non-stressing and stressing thermal environments. This report presents a geometric method for calculating fractal dimensions (D) from time-series datasets of tympanic temperatures, and evaluates the effects of sampling intervals, recording system resolution and noise, and length of sample datasets on the calculated D-value. From these analyses, recommendations were developed for minimum temperature data resolution (0.16 degrees C), sampling interval (3 to 15 min), and data set length (integer multiples of 24-h periods). To reduce the impact of 'noise' in the recording system to less than 5% change in the D-value, the number of errors times the magnitude of the errors (degrees C) should be limited to 0.64 when substituting for missing or questionable data. The fractal dimension computed using the prescribed technique with data collected according to the recommended criteria allows use of all collected data, without requiring removal of underlying deterministic functions or filtering of the data. The method is robust and provides objective differentiation of thermal stress levels in cattle, thereby serving as a basis for environmental evaluation and management. Published by Elsevier Science Ltd.