The etymology of the word cogito literally means "I shake together." The root word is related to our English word agitate. So we could illustrate this with a Descartes shaking ideas together with a cocktail shaker.
Although Descartes actually chose cogito, my favorite image of thinking is actually associated with the alternative word puto, because it derives from a root word meaning "I prune." Thinking involves a lot of pruning, of cutting away clutter. I love the image of Descartes with pruning shears.
But before he wrote in Latin, what he actually wrote in French was "Je pense, donc je suis." The etymology of the French verb penser has nothing to do with either shaking or pruning. It derives from a word that means to weigh or balance. So we could illustrate that with Descartes holding a balance scale with competing ideas piled up on either side.
He didn't write in English, of course, but it is also interesting to consider the etymology of the English verb think. From the Online Etymology dictionary, we have:
Our ability to think is an amazing and multifaceted superpower to reflect upon. We need to shake ideas together, to prune and simplify, to weigh ideas against one another, and to imagine and conceive.
think (v.) Old English þencan "imagine, conceive in the mind; consider, meditate, remember; intend, wish, desire" (past tense þohte, past participle geþoht), probably originally "cause to appear to oneself," from Proto-Germanic *thankjan (source also of Old Frisian thinka, Old Saxon thenkian, Old High German denchen, German denken, Old Norse þekkja, Gothic þagkjan).
