In recent years, aestheticians and philosophers of art have turned their attention towards generative AI — e.g. whether AI systems can be authors or co-authors, whether AI-generated work has any aesthetic merit at all (Wojtkiewicz 2023; Cross 2025). Carlson's aesthetics of natural environments, we argue, offers a productive approach to this territory and opens up the possibility that LLMs themselves can be appreciated. Two temptations should be resisted. The first is to appreciate LLMs as persons. Users talk about a model's ‘personality’ or ‘vibe’, and it is natural to respond aesthetically to these apparent traits. But LLMs lack the temporally extended life, stable dispositions, and projects that underwrite person appreciation. The second is to treat LLMs simply as designed artifacts. LLMs are artifacts, but their aesthetically relevant features — the patterns in their outputs, their characteristic ‘feel’ — emerge from training and from the way generated continuations develop from context, rather than being specified by designers. Order appreciation offers an alternative. Carlson argues that we appreciate nature by attending to patterns produced by natural forces, guided by knowledge — geology, ecology, and the like — that makes those patterns visible. LLMs call for something similar: attention to patterns produced by trained continuation systems, guided by what we call semiotic physics — knowledge of how generated text develops from context under learned constraints. This framework applies at three levels: outputs as bounded continuations, chats as extended exchanges, and models as the trained systems whose tendencies become visible across many outputs and chats. The result is an aesthetics that treats LLMs neither as quasi-persons nor as ordinary tools, but as generative systems with their own characteristic order. Section 1 sets out Carlson's distinction between design appreciation and order appreciation, and considers why person appreciation has to be discussed alongside it. Section 2 asks whether design appreciation can guide the appreciation of LLMs, and argues that LLMs are best understood, for present purposes, as trained continuation systems. Section 3 asks whether person-directed knowledge can guide their appreciation. Section 4 introduces _semiotic physics_ — knowledge of how trained continuation systems develop text from context — as the right kind of knowledge for order appreciation of LLMs. Section 5 shows how this framework guides appreciation at the levels of output, chat, and model.