Found here (top) and here (bottom), via Suddenly.
The scientific explanation for these forms involves Mobius transformations, and is way beyond my sphere of knowledge:
The theorem means that any four such circles that comes with one pairing transformation alpha automatically has another beta. The group generated by these transformations can be applied to the original starting circles to develop a beautiful packing of circles in the plane. If the four circles are all the same size, we simply get the usual hexagonal packing of the plane. But if the circles are of different sizes, we get something a lot more beautiful: a Doyle Spiral. The transformations alpha and beta will be loxodromic spiralling element whirling the circles all around and through each other.I don't know if this helps...
Doyle spiral circle packings (DCSPs) are a rich resource for mathematical investigations with endless applications in computer-based art and design... Each DCSP fills the plane with closely packed circles, where the radius of each circle in a packing is proportional to the distance of its centre from a central point, These packings exhibit many properties – each one is massively self-similar, for example...
ليست هناك تعليقات:
إرسال تعليق