This study identifies new depression biomarkers based on the dynamical properties of tract variables, which represent geometric features describing the configuration of the speech articulators. A key advantage of this approach lies in its ability to quantify aspects of the articulatory process that have not been previously explored in the context of depression, namely predictability, complexity, and randomness. These properties are respectively characterised using the Largest Lyapunov Exponent, the Correlation Dimension, and the Sample Entropy. Thorough experiments were conducted on the Androids Corpus, a publicly available dataset comprising 64 speakers diagnosed with depression by clinicians and 54 control speakers with no reported history of mental health conditions. The results indicate that the proposed biomarkers effectively discriminate between the depressed and control speakers, as evidenced by the high Cliffs delta values across both read and spontaneous speech.