This version is available at https://strathprints.strath.ac.uk/61943/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.