[GIF] Drawing nature with mathematics

[Vitaliyk (Vitaliy Kaurov)]

NOTE: drawn with just circles over a parametric function - a nice animated answer to the below post was given by @Jaebum Jung - formulas and code is below.

with X, Y coordinates and radius dependent as:

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Hamid Naderi Yeganeh is a is a mathematical artist who has a column at The Huffington Post. Recently he wrote:

• Drawing Plants With Mathematics
• Drawing Birds in Flight With Mathematics
• These Are Mathematical Sets

There he produced images (I am sure) reproducible with Wolfram Language. You might potentially come up with your own images. Please post if you have an idea. It is interesting to see how math formulas recreate natural objects.

[jaebum (Jaebum Jung)]

Beautiful! Here’s the one example from post:

xcoord[k_]:=N[(2 k/4000)+(1/28) Sin[(42 Pi k/4000)]+
(1/9) Sin[(21 Pi k/4000)]^8+(1/4) Sin[(21 Pi k/4000)]^6 Sin[(2 \[Pi]/5) (k/4000)^12]]

ycoord[k_]:=N[(1/4) (k/4000)^2+(1/4) (Sin[(21 Pi k/4000)]^5+
(1/28) Sin[(42 Pi k/4000)]) Cos[(Pi/2) (k/4000)^12]]

rad[k_]:=N[1/170-1/67 (-1+Cos[(21 k \[Pi])/4000]^4) Sin[(21 k \[Pi])/2000]^2]

Graphics[{Opacity[.3],RGBColor[0,0.16,0],Table[Circle[{xcoord[i],ycoord[i]},rad[i]],{i,4000}]}]

and with animate

circles = Table[Circle[{xcoord[i], ycoord[i]}, rad[i]], {i, 4000}]; Animate[
 Graphics[{Opacity[.3], RGBColor[0, 0.16, 0], circles[[;; Clip[i, {1, 4000}]]]}, 
  PlotRange -> {{-0.005, 2.28}, {-0.26, 0.44}}, ImageSize -> 600], {i, 1, 4500, 1}, 
 AnimationRate -> 300]