Geometrical Patterns idntification – An investigation

Paper details:

This task/investigation involves Geometrical patterns in Matheamtics. Could you please help me with the task ? I need to find ways of making the task more challenging and find a solution process for the same. Can you help ? Will get more credit if I make he problem more challenging and solve. Report must be about eight (8) pages long including diagrams/sketches. Can you help me with this ? Thanks.