Triple

Target class: Julia set parameter space
Context triple: [Mandelbrot set, instanceOf, Julia set parameter space]

• A. fractal
  A fractal is a complex geometric pattern that exhibits self-similarity at different scales, often generated by repeating a simple process recursively.
• B. generator of PSL(2,ℤ)
  A generator of PSL(2,ℤ) is an element (typically represented by a 2×2 integer matrix modulo ±I) that, together with another such element, produces the entire projective modular group under composition.
• C. conformal model of the hyperbolic plane
  A conformal model of the hyperbolic plane is a geometric representation (such as the Poincaré disk or upper half-plane) in which hyperbolic lines and distances are depicted so that angles are preserved while the metric differs from the Euclidean one.
• D. parabolic element of PSL(2,ℤ)
  A parabolic element of PSL(2,ℤ) is a Möbius transformation represented by an integer 2×2 matrix of determinant 1 with trace ±2, which fixes exactly one point on the extended real line (typically a rational cusp) and acts there by translation.
• E. tool in dynamical systems theory chosen
  A tool in dynamical systems theory is a conceptual or computational method—such as phase portraits, Lyapunov functions, or Poincaré maps—used to analyze, visualize, and understand the qualitative and quantitative behavior of dynamical systems over time.
• F. None of above.