Infinite families of tangent circles. More here

Pickover's Popcorn fractal rendered using a triangular variation of the Hilbert space-filling curve.
By Kerry Mitchell

Visualizing Conformal Mapping

Beautiful works by Samuel Monnier visually exploring the Lattès map
  

Limit set

Limit set of a group determined by a thrice punctured sphere
By David Dumas

Twin Snowflakes

     "Since each snowflake faces a different turbulent path through the atmosphere, each twist, turn and fall grants it a unique symmetry. But if you subtract nature’s volatility from the equation, then these icy flowers are no longer guaranteed uniqueness.

     By placing two crystal seeds next to each other and growing them under the exact same conditions, Dr. Libbrecht found that he could create two snowflakes with nearly the same intricate shapes and patterns."

Twin snowflakes, grown from crystals under the same temperature and humidity conditions, surrounded by water droplets.  (Kenneth Libbrech)