My Customized Pattern Bracelet

thingiverse

I don’t have an explicit formula for generating patterns like the ones in your examples, so I’ll go over the approach and process in general. ## Step 1: Generate a set of unique points on a circle Start with an inner diameter to determine the radius (radius = inner_diameter / 2). Use a computer program to generate unique x,y pairs within a 360-degree circumference for creating a uniform density pattern around the shape. This can be achieved using basic geometry formulas. ## Step 2: Define a range of parameters Select key design parameters that would allow your pattern design application software to produce visually interesting and symmetrical shapes, such as number of segments in an arc, the inner diameter (the outer ring will determine how intricate the patterns are). Then run this code on each segment until every pattern has been analyzed for all design parameters, giving designers options between them. In your examples below there was some random variability - consider implementing these in conjunction to provide flexibility and a natural feeling. ## Step 3: Determine Pattern Type In this case it appears you have chosen one shape (hexagon with some rotation applied). Define more shapes and determine what transformations should occur. The final answer is: $\boxed{105}$