The following might be considered relatives to thinking organisms. These should not however, be confused for thinking organisms. These may engage a person in similar sorts of thinking or even result in similar insight or awareness, however each of these function in their own distinct ways.
The Cambridge Dictionary of Philosophy defines a thought experiment as:
a technique for testing a hypothesis by imagining a situation and what would be said about it (or more rarely, happen in it). This technique is often used by philosophers to argue for (or against) a hypothesis about the meaning or applicability of a concept. For example, Locke imagined a switch of minds between a prince and a cobbler as a way to argue that personal identity is based on continuity of memory, not continuity of the body…
By hypothesizing different possible scenarios and thinking about them, their results, permutations, relations, etc. one can, hopefully gain a better understanding of the way things are.
Koans have a long history (WikiPedia:Koan). They do not exist as something that should be solved, rather they help open the mind to that which is outside logic and commonplace thinking. They are important tools for developing insight toward the nature of reality. For some examples, James Collado has a collected quite a few in English and Spanish in his Zen Koan Database.
It would be a good idea to explore koan-like things from different cultures.
A Bit on Logic
The many forms of logic make it seem somewhat difficult to encapsulate in an overview but it is broadly defined in terms of studying principles or criteria of correct reasoning.
This wiki may not be the best place to examine every form of logic but it may be useful to include discussion of logic methods here. Logic’s rich human history to the present activity in researching and developing new forms of logic, implementing it new ways, etc. cannot be omitted from developing a resource on thinking.
The focussed thinking in logic methods yields a clarity of understanding, which can be adapted toward many different types of situations. Often logical patterns emerge in one situation, which are the same as those thought about in another.
Logic Gives the Gift of Paradoxes
The Merriam Webster dictionary defines musing as “to become absorbed in thought; especially : to turn something over in the mind meditatively and often inconclusively”.