  We realize fractal-like photonic lattices using cw-laser-writing technique,
thereby observe distinct compact localized states (CLSs) associated with
different flatbands in the same lattice setting. Such triangle-shaped lattices,
akin to the first generation Sierpinski lattices, possess a band structure
where singular non-degenerate and nonsingular degenerate flatbands coexist. By
proper phase modulation of an input excitation beam, we demonstrate
experimentally not only the simplest CLSs but also their superimposition into
other complex mode structures. Furthermore, we show by numerical simulation a
dynamical oscillation of the flatband states due to beating of the CLSs that
have different eigenenergies. These results may provide inspiration for
exploring fundamental phenomena arising from fractal structure, flatband
singularity, and real-space topology.
