REACTION- DIFFUSION PATTERNS

• Labyrinthine pattern

  An initial stripe is unstable to transverse perturbations and grows. The stripe meanders and undergoes tip-splitting until a final stationary labyrinthine pattern is reached.

• Spiral breakup

  A spiral wave, intially computed in a stable parameter regime, breaks and a new pattern emerges where new spiral waves are continuously created and destroyed.

• Spiral breakup 2

  A spiral wave, intially computed in a stable parameter regime, breaks and a new pattern emerges where new spiral waves are continuously created and destroyed.

• Spiral turbulence

  An almost planar pluse is unstable to transverse perturbations. Cusps form along the front line and nucleate pairs of new spiral waves. The spirals are unstable and break, creating new spiral pairs.

• Spot splitting

  A small spot grows, splits into two spots, and eventually fills the entire domain with a disconnected labyrinthine pattern

• Spot splitting 2

  A small spot grows, splits into two spots, and eventually fills the entire domain with a disconnected oscillating labyrinthine pattern. The long-time behavior of this pattern is unknown.

• Spiral breakup by an external advective field

  A spiral wave is subjected to a weak hexagonal advective field and breaks to form many new spiral tips.

• "From labyrinthine patterns to spiral turbulence"
  
• "Complex patterns in reaction-diffusion systems: A tale of two front instabilities"
  
• "Pattern formation in non-gradient systems: the effects of front bifurcations"
  
• "Domain walls in nonequilibrium systems and the emergence of persistent patterns"
  
• "Fronts and patterns in reaction-diffusion equations"
  
• "Dynamic front transitions and spiral-vortex nucleation"