This drawing is actually found on the back of a tablet listing female goats (PY Cn 1287). Apparently the scribe found this list pretty boring, or perhaps they were kept hanging around waiting for whoever was bringing the information about the goats in question. Either way, they doodled this labyrinth on the back. It’s actually a reasonably complicated design – I had to trace it out on the icing to be sure of getting it to work, and the 1965 Cambridge Mycenaean Colloquium even featured a paper on how it could have been constructed* – and yet is drawn pretty neatly, so perhaps this was this scribe’s regular doodle of choice…? This isn’t unique as a doodle, by the way; there’s the odd drawing of a person or animal, plus a couple of tablets with a sequence that might (possibly) be the Mycenaean equivalent of an abecedary, giving the order of the first few syllabic signs in the sequence the scribes learned them.
Of course, what’s simultaneously frustrating and interesting about this is that it comes from Pylos – not Knossos, the home of the famous Labyrinth, built by Daedalus and inhabited by the Minotaur. We do, however, have some texts from Knossos that might add to the picture. KN Fp 1, a list of offerings of olive oil being sent to various sanctuaries, deities, and religious personnel, includes an entry da-da-re-jo-de, interpreted pretty plausibly as Daidaleion-de: ‘to the shrine of Daedalus’. Two other tablets (KN Gg 702 and Oa 745) have the entry da-pu2-ri-to-jo , po-ti-ni-ja, also a recipient of offerings. po-ti-ni-ja is clearly Potnia, ‘mistress/lady’, following a term in the genitive: so ‘Lady of the da-pu2-ri-to‘. And this second term is generally interpreted as laburinthos, the Labyrinth.
Before you start saying, wait a minute, it doesn’t look anything like that, it’s not quite as problematic as you think: as the Linear B script doesn’t normally distinguish voicing or aspiration or write syllable-final n, -ri-to would be the regular spelling for -rinthos, and pu2 can quite plausibly represent bu. The first syllable is a bit more difficult, but this is clearly a word of non-Greek origin – it doesn’t have an Indo-European etymology, -nthos is quite a frequent suffix on non-Greek loanwords, and there’s a possible connection with the word labrus, quoted by Plutarch (Moralia 302a) as being a Lydian word for ‘axe’ (and yes, this is as dodgy as you think it is and leads to all sorts of speculation about the Minoan House of the Double Axes which I’m not going to go into). Anyway, alternation between d and l in non-Greek loanwords is a reasonably common feature – cf. Odysseus/Ulysses – and it’s possible (though by no means certain or unproblematic) that Minoan (the language Linear A was used to write, and presumably the origin of most of the non-Greek words found in Knossian Linear B) had a single sound midway between d and l rather than a distinction between the two, leading to different interpretations by different Greek-speakers.
So, we have some possible evidence for the existence of a labyrinth story at Mycenaean Knossos – though obviously what form(s) this story might have taken, e.g. whether Daedalus was even linked to the labyrinth at this period, is unknowable – and it’s tempting to say that the Pylos labyrinth shows that other Mycenaean sites also had a version of this story. On the other hand, labyrinth drawings seem to be found not just all round the early Mediterranean but also elsewhere in the world, and while those from the Classical Greek and Roman periods are generally inspired by the Knossian myth as we know it today (e.g. the labyrinth coins from Knossos, or the Pompeiian labyrinth graffito), others are far too early and/or far away for this. Perhaps there were a lot of different labyrinth stories that haven’t survived – after all, labyrinths have been interpreted and used in plenty of different ways since ancient times. Or, perhaps, this type of pattern is just one that people like to draw. Regardless of any speculation about Minoan or Mycenaean labyrinths (which you’re free to dismiss completely as nonsense if you want), I’d say both are probably likely to be true.
*L.J.D. Richardson, ‘The Labyrinth’, in L.R. Palmer & J. Chadwick, eds, Proceedings of the Cambridge Colloquium on Mycenaean Studies (C.U.P., 1966), 285-296 (whose conclusions regarding the relationship of the Pylos labyrinth to Irish stone carvings are, however, to be taken with at least a pinch of salt).