Abstract An analysis of the temperature factors of an abenzyme has been performed to gain information on the possible role of deterministic chaos in the catalytic mechanism of such artificial proteins. The H-chain displayed a regular attractor of the dimension 3.0 ± 0.3, whereas the L-chain showed one of 〈 d〉=7.5±0.5. The abenzyme also displayed a stochastic attractor of the dimension ca. 0.9. The H-chain attractor has one dimension more than those of the native hydrolases chymotrypsin and lysozyme. The additional degree of freedom of the abenzyme offers a likely explanation of the low specific catalytic activities of these artificial enzymes. The dimension of the attractor in the L-chain falls in the range found for other antibodies. Hence, a clear dichotomy seems to rule in this abenzyme; the H-chain displays the vibrational properties of an enzyme and the L-chain those of an antibody. The new data supports the hypothesis of an important role of attractors in biochemical mechanisms by reduction of the number of degrees of freedom (entropy) of reaction partners. A hierarchy of attractors is associated with specific protein functions.