Gregg Helt

This piece started with four tangent circles of equal radius in a 4-fold rotational symmetry, and a centered eight petal rhodonea curve intersecting all four circles. I defined four circle inversion transformations based on the circles, and also defined a rhodonea inversion transformation using a recently introduced method for generalizing inversion to certain non-circular shapes. Then I applied a new technique of mixed location-dependent restrictions for iterating inversions using an iterated function system (IFS), and starting from a random point. Points were colored along a gradient based on proximity to the perimeter of the last circle or rhodonea inversion applied. Five smaller copies of the whole were added for aesthetic appeal.

This piece started with seven overlapping circles of equal radius, with six in a 6-fold rotational symmetry surrounding a central circle in a configuration known as the "Seed of Life" that has been used in decorative designs since ancient times. For each circle I defined a circle inversion transformation. Then I applied a new technique of mixed location-dependent restrictions for iterating inversions using an iterated function system (IFS). Iteration was started both from random points and from points taken from the circle perimeters. The inner hexagon and other straight lines are the result of inversions of circle perimeters that pass through the center of the inverting circle.