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RandomWalks.jl
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RandomWalks.jl
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### A Pluto.jl notebook ###
# v0.16.1
using Markdown
using InteractiveUtils
# ╔═╡ 03257750-42df-11ec-0e39-f16f40d295c9
begin
using Javis, Animations, StatsBase
end
# ╔═╡ da610f95-c5bd-49ce-a199-d7896b635b08
function randomWalk(numsteps = 100)
moves = [Point(0, 1), Point(0, -1), Point(1, 0), Point(-1, 0)]
traj = accumulate(sample(moves, numsteps - 1), init = Point(0, 0)) do old, move
old + move
end
return vcat(Point(0, 0), traj)
end
# ╔═╡ 46351f65-5d77-46c5-9f56-bbe4064f6f17
md"""
## Single particle
"""
# ╔═╡ 12cb472f-f9e6-4031-bc67-da0aa2f33a05
let
function ground(args...)
background("black")
sethue("white")
end
function draw_line(p1 = O, p2 = O, color = "black", action = :stroke, edge = "solid")
sethue(color)
setdash(edge)
setline(1)
line(p1, p2, action)
end
function circ(p = O, color = [1.0, 1.0, 1.0], alph = 1.0, action = :fill, radius = 25, edge = "solid")
setcolor(color..., 0.6)
setdash(edge)
circle(p, radius, action = :stroke)
setcolor(color..., alph)
circle(p, radius, action)
return p
end
function path!(points, pos, color)
push!(points, pos) # add pos to points
draw_line.(points[2:end], points[1:end-1], color)
end
nframes = 300
cut_off = 200
fade_time = 50
col = [0.0, 0.0, 1.0]
myvideo = Video(500, 500)
Background(1:nframes, ground)
r = 5
bpath = randomWalk(cut_off)
path_of_ball = Point[]
banim = Animation(
range(0, stop = 1, length = cut_off),
10*bpath,
linear())
ball = Object(1:nframes, (args...) -> circ(O, [0.0, 0.0, 0.7], 0.9, :fill, r), Point(0, 0))
act!(ball, Action(1:cut_off, banim, translate()))
ball_traj = Object(1:cut_off + fade_time, (args...)->path!(path_of_ball, pos(ball), "blue"))
act!(ball_traj, Action(cut_off: cut_off + fade_time, disappear(:fade)))
render(
myvideo;
pathname="SHM.gif")
end
# ╔═╡ 5d1c1e58-8693-4d7b-83f1-36e37aa2e7f3
md"""
## Multiple particles
"""
# ╔═╡ 585605d9-d895-43c4-b037-5b25e4e01793
let
function ground(args...)
background("black")
sethue("white")
end
function draw_line(p1 = O, p2 = O, color = "black", action = :stroke, edge = "solid")
sethue(color)
setdash(edge)
setline(1)
line(p1, p2, action)
end
function circ(p = O, color = [1.0, 1.0, 1.0], alph = 1.0, action = :fill, radius = 25, edge = "solid")
setcolor(color..., 0.6)
setdash(edge)
circle(p, radius, action = :stroke)
setcolor(color..., alph)
circle(p, radius, action)
return p
end
function path!(points, pos, color)
push!(points, pos) # add pos to points
draw_line.(points[2:end], points[1:end-1], color)
end
nframes = 250
cut_off = 150
fade_time = 50
col = [0.0, 0.0, 1.0]
myvideo = Video(300, 300)
Background(1:nframes, ground)
r = 1.5
num_walkers = 10
bpath = [randomWalk(cut_off) for i in 1:num_walkers]
path_of_ball = [Point[] for i in 1:num_walkers]
ball_traj = []
banim = Animation.(
[range(0, stop = 1, length = cut_off)],
3 .* bpath,
[linear()])
ball = [Object(1:nframes, (args...) -> circ(O, [0.0, 0.0, 0.7], 0.9, :fill, r), Point(0, 0)) for i in 1:num_walkers]
for i in 1:num_walkers
act!(ball[i], Action(1:cut_off, banim[i], translate()))
push!(ball_traj, Object(1:cut_off + fade_time, (args...)->path!(path_of_ball[i], pos(ball[i]), "blue")))
act!(ball_traj[i], Action(cut_off: cut_off + fade_time, disappear(:fade)))
end
render(
myvideo;
pathname="SHM.gif")
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Animations = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
Javis = "78b212ba-a7f9-42d4-b726-60726080707e"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
[compat]
Animations = "~0.4.1"
Javis = "~0.7.1"
StatsBase = "~0.33.12"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libglvnd_jll]]
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[[Libgpg_error_jll]]
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[[Libiconv_jll]]
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[[Libmount_jll]]
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[[Librsvg_jll]]
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[[Libtiff_jll]]
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[[Libuuid_jll]]
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[[LightXML]]
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[[LinearAlgebra]]
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[[LogExpFunctions]]
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[[Logging]]
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[[Luxor]]
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[[MKL_jll]]
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[[MacroTools]]
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[[MbedTLS]]
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[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
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[[Measures]]
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[[Mmap]]
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[[MosaicViews]]
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[[MozillaCACerts_jll]]
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[[NaNMath]]
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[[Netpbm]]
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[[Observables]]
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[[OffsetArrays]]
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[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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[[OpenEXR]]
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[[OpenEXR_jll]]
deps = ["Artifacts", "Imath_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
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[[OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
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[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
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[[OpenSpecFun_jll]]
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[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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[[OrderedCollections]]
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[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
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[[PNGFiles]]
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[[PaddedViews]]
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