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I found this image online:
and I would like to recreate it in mathematica. Is there an easy way to create this kind of circle packing in mathematica wihtout calculating all the individual radii? I found multiple examples of circle packings in mathematica but they are all based on using the same radius for each packed circle.
An alternative interpretation of the question: let's be lazy and compute the circles' pattern from the image.
img=Import["https://i.stack.imgur.com/kDMPt.png"]
ctds=#2&@@@ComponentMeasurements[{img,MorphologicalComponents[
img,.6]},"Centroid",Abs[#Circularity-1]<.1\[And]#Area>200&]
Most of the triangles have area <200, and all the circles have area >200. I used HighlightImage[img,ctds] to see this,
The thickness of the lines seems consistent, so adding 2 (about the thickness of the lines, in pixels) to each radius seems to work:
Graphics[Circle[#[[2,1]],#[[2,2]]+2]&/@ComponentMeasurements[
{img,MorphologicalComponents[img,.6]},{"Centroid",
"EquivalentDiskRadius"},Abs[#Circularity-1]<.1\[And]#Area>200&]]
This is quick and dirty. In reality, intuition+Mathematica (as opposed to just asking Mathematica to numerically find centroids) is a more beautiful thing. I think it'd be pretty quick to bin the radii and centers along precise circles (they vary by ~.2 pixels due to anti-aliasing).
