In nature, the way a system behaves often depends on multiple competing factors. This is particularly apparent for chemical reactions, some of of which can oscillate in wild patterns as different forces compete. Similar patterns can occur in combustion, as shown above.
What you see here are patterns formed on a flame propagating down a tube. They’re a result of what’s known as a thermal-diffusive instability. Flames like these typically propagate by conducting heat into the fuel-air mixture ahead of the flame front, thereby raising its temperature, while, simultaneously, fuel and air diffuse into the flame to sustain the chemical reactions. If the rates of heat transfer and chemical diffusion are balanced, the flame moves steadily. But if there’s an imbalance between those factors, instabilities occur.
In this case, the temperature rises much faster than the time needed for fresh fuel to move into the flame. As the temperature goes up, the reaction rate increases exponentially, and the flame surges forward. But the slow resupply of fuel makes the reaction rate drop, causing the flame’s progress to stall. This interplay results in the complex, pulsating instabilities we see here. (Image and submission credit: H. Pearlman; research credit: H. Pearlman and D. Ronney)