学术报告（Izumi Takagi 12.10）
Is this what Turing tried to say?
In his last paper, Alan M. Turing considered how patterns were formed without external manupilation in developing biological systems. He proposed the notion of Diffusion Driven Instability (DDI) to explain the spontaneous formation of pattern as a result of destabilization of spatially uniform states caused by different diffusion rates.
Nowadays patterns emerging from uniform states due to DDI are called Turing patterns. Mathematically speaking, behind this terminology, the occurrence of bifurcation of nonconstant steady-states from a constant steady-state is implicitly assumed.
In this talk, we show by examples that (i) patterns can be obtained without bifurcation, and (ii) even if there does occur bifurcation, all nonconstant bifurcating solutions can be unstable. We go back to his paper and try to redefine "pattern formation" in Turing's context.