Cat
The domestic cat has refined unpredictability to a behavioural science. Its actions follow no discernible pattern, respond to no identifiable stimulus, and serve no apparent purpose beyond the pure expression of feline autonomy. A cat may demand attention with theatrical urgency, only to lose interest the moment it is provided. It may sprint through the house at 3am pursuing invisible prey, or spend fourteen hours motionless in a sunbeam. Studies attempting to predict cat behaviour have produced results indistinguishable from random number generators. The cat has achieved something remarkable: unpredictability so complete that even the cat itself appears surprised by its own actions. This chaos operates continuously, requiring no planning and producing no explanations.
The Joker
The Joker's unpredictability is a carefully cultivated philosophy rather than a natural state. He commits considerable resources to ensuring his actions remain incomprehensible, constructing elaborate schemes designed to defy logical analysis. His randomness is, paradoxically, deliberate and intentional. He might release hostages or eliminate them; he might explain his motivations or provide contradictory accounts. Gotham's analysts have dedicated careers to predicting his behaviour, producing volumes of utterly useless documentation. Yet The Joker's chaos requires effort, planning, and theatrical execution. He must actively work to be unpredictable, whilst the cat achieves this state simply by existing.
VERDICT
The cat achieves effortless, continuous unpredictability without apparent intent or planning. The Joker must work at his chaos; the cat simply is chaos.