Surfing on the net I stared at this pattern. It´s a bamboo steam, and it´s awesome. I'm new to Mathematica so I'm a little lost, I'd like to try to reproduce this pattern, of course in a very simplified manner. Does anyone have any tips on how I could start it. Thanks..
bambusa_steam http://www.quorumtech.com/media/image_gallery/cache/Bamboo_stem.jpg
Here's an approach based on generating a set of points (the centres of the voids) and using a DistanceTransform:
i=Image[Graphics[{White,Disk[{0,0},1],Black,
Point@Flatten[Table[r^(1/4) {Sin[t],Cos[t]},{r,0.001,1,0.1},{t,0.001,2Pi,0.025/r}],1],
Point@Table[RandomReal[{0.2,1}]Through[{Sin,Cos}[RandomReal[{0,2Pi}]]],{1000}]},
Background->Black],ImageSize->500];
i2=ImageMultiply[DistanceTransform[i],0.1];
i3=ColorNegate@GaussianFilter[Binarize[i2,1.0],4];
ImageAdjust[ImageMultiply[i2,i3]]
I'm not sure exactly what you mean by recreate using Mathematica but here is a quick image process/computational geometry based method.
I imported the image:
image = Import["http://www.quorumtech.com/media/image_gallery/cache/Bamboo_stem.jpg"]
Ran an edge detection filter and then isolated the individual components
m = MorphologicalComponents[EdgeDetect[image]]; m // Colorize
Then determine the centroid of the components
points = ComponentMeasurements[m, "Centroid"][[All, 2]];
Then compute a voronoi diagram of the points (you could alter these points to adjust the structure in mathematica)
Needs["ComputationalGeometry`"];
DiagramPlot[points, TrimPoints -> 500, LabelPoints -> False]
Maybe this code that I wrote long time ago (so, the inefficiency is included for free) might be what you're looking for.
circleIntersect[x1_, y1_, r1_, x2_, y2_, r2_] := Module[
{dx, dy, distance},
dx = x1 - x2;
dy = y1 - y2;
distance = Sqrt[dx*dx + dy*dy];
r1 + r2 >= distance
]
theCircle = {{0, 0}, 50};
crit[x1_, y1_, r1_] := Module[{dist},
dist = Sqrt[x1*x1 + y1*y1] + r1;
dist >= theCircle[[2]]
]
newCircle0[] := {{RandomReal[{-50, 50}], RandomReal[{-50, 50}]},
RandomReal[{0.5, 4}]};
newCircle[] := Module[{temp},
While[
temp = newCircle0[];
crit[temp[[1, 1]], temp[[1, 2]], temp[[2]]]
];
temp]
circleList = {newCircle[]};
noList = {};
For[j = 0, j < 10000, j++,
c = newCircle[];
r = Table[
circleIntersect[c[[1, 1]], c[[1, 2]], c[[2]],
circleList[[i, 1, 1]], circleList[[i, 1, 2]],
circleList[[i, 2]]], {i, Length[circleList]}];
If[Count[r, True] > 0,
noList = Append[noList, c],
circleList = Append[circleList, c]];
]
circleList;
Show[{Graphics[Circle[{0, 0}, 50]],
Graphics[
Table[Circle[{circleList[[i, 1, 1]], circleList[[i, 1, 2]]},
circleList[[i, 2]]], {i, Length[circleList]}]]}]
Higher is the value of j in the for-loop, more densely packed will be the circles (and more time it will take).
You could think of this as an inverse cellular automaton problem, where the goal is to find a cellular automaton that generates the (type of) pattern that you showed. It might be worth having a look at Cellular Automata, Theory and Experiment, Edited by Howard Gutowitz - http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=4479 - where the description says:
"The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole."
