Recent advances in design theory help clarify the logic, forms and conditions of generativity. In particular, the formal model of forcing predicts that high-level generativity (so-called generic generativity) can only be reached if the knowledge structure meets the 'splitting condition'. We test this hypothesis for the case of Bauhaus (1919–1933), where we can expect strong generativity and where we have access to the structures of knowledge provided by teaching. We analyse teaching at Bauhaus by focusing on the courses of Itten and Klee. We show that these courses aimed to increase students' creative design capabilities by providing the students with methods of building a knowledge base with two critical features: 1) a knowledge structure that is characterized by non-determinism and non-modularity and 2) a design process that helps students progressively 'superimpose' languages on the object. From the results of the study, we confirm the hypothesis deduced from design theory; we reveal unexpected conditions on the knowledge structure required for generativity and show that the structure is different from the knowledge structure and design process of engineering systematic design; and show that the conditions required for generativity, which can appear as a limit on generativity, can also be positively interpreted. The example of Bauhaus shows that enabling a splitting condition is a powerful way to increase designers' generativity.