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[GIF] Drawing nature with mathematics

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.

enter image description here

with X, Y coordinates and radius dependent as:

enter image description here



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

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.

enter image description here

enter image description here

POSTED BY: Vitaliy Kaurov
Posted 9 years ago

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}]}]

enter image description here

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]

enter image description here

POSTED BY: Jaebum Jung
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