345 lines
9.1 KiB
Julia
345 lines
9.1 KiB
Julia
### A Pluto.jl notebook ###
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# v0.19.25
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using Markdown
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using InteractiveUtils
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# ╔═╡ 9be49371-fcb2-4434-8377-e9c4702a04d3
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using PyPlot
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# ╔═╡ c0a23ac6-f4df-11ed-10d7-e5ce8a11a112
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md"""
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# 1- Fractals
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The first excersice is to draw Koch's curve. In the function `segPoints(startPoint, endPoint, n = 3)`, we divide the given into `n` equal segments.
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Then we need a third point to make a equilateral triangle (for now. But we will generalise this algorithm to make other forms of Koch's curve-like fractals.). The function `polygon(startPoint, endPoint, n=3)` will make the triangle (by default).
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"""
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# ╔═╡ 07bae7e7-a136-428f-ad80-91f63c7c5d90
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begin
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# To divide a line into n segments
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function seg_points(startPoint, endPoint, n=3)
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mids = []
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for i in 1:n-1
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push!(mids, (1-i/n) * startPoint + i/n * endPoint)
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end
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return mids
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end
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# To define triangle in the mid segment
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function polygon(p1, p2, n=3)
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x = p2[1]-p1[1]
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y = p2[2]-p1[2]
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P3 = p1 + [x * cos(pi/3) - y * sin(pi/3), x * sin(pi/3) + y * cos(pi/3)]
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return P3
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end
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end
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# ╔═╡ 56faf886-32df-4621-92be-742eb1e94a79
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# Draw!
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function koch_curve(order::Int, startPoint = [0.0,0.0], endPoint = [1.0,0.0])
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pts=[startPoint, endPoint]
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for i in 1:order
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order_points =[]
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for j in 2:length(pts)
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a = pts[j-1]
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b = pts[j]
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c, d = seg_points(a, b)
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e = polygon(c, d)
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push!(order_points, a, c, e, d)
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end
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push!(order_points, pts[end])
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pts = order_points
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end
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return pts
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end
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# ╔═╡ faf602cf-9c69-45b7-9a0a-6168ad9ca02b
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begin
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points = koch_curve(5)
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X = [pt[1] for pt in points]
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Y = [pt[2] for pt in points]
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plot(X, Y, linewidth=0.5)
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axis("equal")
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show()
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end
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# ╔═╡ 00000000-0000-0000-0000-000000000001
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PLUTO_PROJECT_TOML_CONTENTS = """
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[deps]
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PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee"
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[compat]
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PyPlot = "~2.11.1"
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"""
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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PLUTO_MANIFEST_TOML_CONTENTS = """
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# This file is machine-generated - editing it directly is not advised
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"""
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# ╔═╡ Cell order:
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# ╟─c0a23ac6-f4df-11ed-10d7-e5ce8a11a112
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# ╠═9be49371-fcb2-4434-8377-e9c4702a04d3
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# ╠═07bae7e7-a136-428f-ad80-91f63c7c5d90
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# ╠═56faf886-32df-4621-92be-742eb1e94a79
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# ╠═faf602cf-9c69-45b7-9a0a-6168ad9ca02b
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# ╟─00000000-0000-0000-0000-000000000001
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# ╟─00000000-0000-0000-0000-000000000002
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