@juliohm, yes, I am using the GR backend. Other info: Win10 Julia 1.5.3, GR v0.53.0, Plots v1.9.1. Thanks for the tips and for the offer to look at it. I will reach out on separate channel after doing some more homework on this.
Like with Julia, experts say that Shakespearean language can be tricky but that acting it out makes it fun and understandable. On the same vein, the following MIT list of Shakespearean insults might be a good way to learn both languages:
using CSV, DataFrames, HTTP f = CSV.File(HTTP.get("http://web.mit.edu/dryfoo/Funny-pages/shakespeare-insult-kit.html").body); sk = DataFrame(f[17:66]) # TODO: findfirst "artless" word to set range r = size(sk,1) sk = DataFrame([split(sk[i,1]) for i in 1:r]) # output = 3 rows x 50 columns Shakespeare() = println("Thou "*sk[1,rand(1:r)]*" "*sk[2,rand(1:r)]*" "*sk[3,rand(1:r)])
Then call Shakespeare:
julia> Shakespeare() Thou artless beef-witted joithead julia> Shakespeare() Thou villainous motley-minded giglet
With 15 lines I could write a code to perform a particle simulation with periodic boundary conditions, a langevin thermostat, and a quadratic potential between the particles, and produce an animation:
using Plots ; ENV["GKSwstype"]="nul" const N, τ, Δt, λ, T, k = 100, 1000, 0.01, 1e-3, 0.26, 1e-6 const x, v, f = -0.5 .+ rand(3,N), -0.01 .+ 0.02*randn(3,N), zeros(3,N) wrap(x,y) = (x-y) > 0.5 ? (x-y)-1 : ( (x-y) < -0.5 ? (x-y)+1 : (x-y) ) anim = @animate for t in 1:τ f .= 0 for i in 1:N-1, j in i+1:N f[:,i] .+= wrap.(x[:,i],x[:,j]) .- λ .* v[:,i] f[:,j] .+= wrap.(x[:,j],x[:,i]) .- λ .* v[:,j] end x .= wrap.(x .+ v*Δt .+ (f/2)*Δt^2,zeros(3)) v .= v .+ f*Δt .+ sqrt.(2*λ*k*T*Δt)*randn() scatter(x[1,:],x[2,:],x[3,:],label="",lims=(-0.5,0.5),aspect_ratio=1,framestyle=:box) end gif(anim,"anim.gif",fps=10)
As Tamas mentioned, if we go to a few more lines, this could include an actual Lennard-Jones potential and be parallelized. And that without using any package besides Plots.
I love watching particles dance! Awesome Leandro!
Infinizoom! (Background: Simulates a Brownian motion and uses the Brownian self-similarity https://en.wikipedia.org/wiki/Wiener_process#Self-similarity combined with simple data-augmentation/Brownian bridge sampling to zoom in infinitely.)
using Makie dt = 0.0005; ϵ = 0.1; t = collect(-1.0:dt:1.0); n = length(t) x = sqrt(dt)*cumsum(randn(n)); x .-= x[end÷2] T, X = Node(t), Node(x) p = lines(T, X); display(p) xlims!(-1.0, 1.0); ylims!(-1.5,1.5) while true t .*= (1 + ϵ) x .*= sqrt(1 + ϵ) if t[end] > 2.0 t .= collect(-1.0:dt:1.0) x[1:2:end] = x[n÷4+1:3n÷4+1] x[2:2:end] = (x[1:2:end-2]+x[3:2:end])/2 + sqrt(dt)/2*randn(n÷2) x[end÷2+1] = 0 end T = t; X = x; sleep(0.02) end
xc, yc = -0.55, 0.61; x0, x1 = xc - 2, xc + 2; y0, y1 = yc - 2, yc + 2; anim = @animate for t in 1:50 x, y = range(x0, x1; length=1000), range(y0, y1; length=1000) heatmap(x, y, -log.(mandelbrot.(x' .+ y .* im));aspect_ratio=1,border=:none,legend=:none); x0, x1 = (15x0 + x1)/16, (15x1 + x0)/16; y0, y1 = (15y0 + y1)/16, (15y1 + y0)/16 end gif(anim,"mandelbrot_zooms.gif",fps=10)
for reference, what is the extended code that gives your example (a) parallelized (b) with the actual L-J potential © both
Nice! I was thinking of doing something similar, but I couldn’t find the time, nor fit it in less than 7 lines (you cheated! ).
I think that, to make it better, the number of iterations in
mandelbrot has to increase the more one zooms in, otherwise the boundary of the fractal becomes too imprecise. Here is a complete version that does so:
using Plots exprange(start, stop, len) = exp.(range(log(start), log(stop), length=len)) function mandelbrot(z; lim=75) w = z for n = 1:lim; abs2(w) < 4 ? w = w^2 + z : return n end lim + 1 end x₀, y₀ = -0.5626805, 0.6422555 anim = @animate for (r, l) in zip(exprange(2, 1.35e-6, 120), exprange(100, 2500, 120)) x = range(x₀-r, x₀+r; length=600); y = range(y₀-r, y₀+r; length=600); heatmap(x, y, -log.(log.(mandelbrot.(x' .+ y .* im; lim=round(l)))); legend=:none, border=:none, ticks=:none, size=(600,600), ratio=1) end g = gif(anim; fps=12)
Apparently I cannot attach the animated GIF file (which you can find here), so I include only the last frame:
Calculating a cross-correlation in any number of dimensions:
for I in CartesianIndices(img) for J in CartesianIndices(kernel) # kernel with centered indices if I+J in CartesianIndices(img) filtered[I] += img[I+J] * kernel[J] end end end
The code in action:
using OffsetArrays using Makie # A 3D "image" of random values (either 0 or 1) img = rand([0.0, 1.0], 20, 60, 40) # Plot s1 = volume(img, algorithm=:iso, resolution=(800, 500)) # Function to generate an N-dimensional kernel of uniform values that sum to 1 # The center of the hypercube will have indices (0, 0, ..., 0) uniform_kernel(n, dim) = OffsetArray(fill(1/n^dim, fill(n, dim)...), fill(-n÷2-1, dim)...) # 5x5x5 array of uniform values that sum to 1 kernel = uniform_kernel(5, 3) # 3 dimensions filtered = zero(img) for I in CartesianIndices(img) for J in CartesianIndices(kernel) if I+J in CartesianIndices(img) filtered[I] += img[I+J] * kernel[J] end end end s2 = volume(filtered, algorithm=:iso, resolution=(800, 500))
What about a simulation with balls bouncing against each other?
Or a simulation of moving people getting infected with a virus when they meet other people.
I have one of those, but not in a compact code.
From here: https://github.com/m3g/CKP
@LaurentPlagne posted this beautiful example:
See Plot a circle with a given radius with Plots.jl. I don’t know if he has published the code for it though.
] activate . instantiate
This is some of my favorite Julia code.
Thank you for the comment
Unfortunately I don’t think that it can fit the 7 lines example list (>1000 SLOC)…
We use this example to show how to structure a not-too-small project (PkgSkeleton, types, modules, sub-modules, tests, export, dependencies, multiple dispatch, profile, //isme …) in our Julia training lectures.
Although I enjoy reading the examples in this thread, I would second @Tamas_Papp saying that Julia’s power is more strongly demonstrated through slightly larger examples.
We must take some time to refactor the package from its training material form and publish it : now I have an extra motivation to see if a Julia wizard could compact it significantly
Side note: Love the color scheme. What are you using for it?
I think seven lines of code is excellent. It showcases what Julia can do, and hopefully shows how Jukia can express scientific notation or equations in a compact way.
However one small pleading from me. Let’s now go down the road of Obfuscated Perl. Back in the day when Perl was a dominant language for Web programming, and many other things, there were a lot of smart people involved. Still are probably! There were regular ‘Obfuscated Perl’ competitions.
Also the whitespace as code stuff (where you translate code into …err… meaningful whitespace ) etc.
I know I am being like the Grinch but IMHO these did the language no good
Don’t get me wrong - there is nothing bad about using a language feature but please, please explain what it does so other people can learn.
I recently started using SatelliteToolbox.jl, so here is my submission. This code calculates the location (latitude, longitude, altitude) of the ISS “right now”. The readability suffers a bit trying to stick to seven, but it’s not too bad. This is based off of the example here (see the link for full details).
using Dates, SatelliteToolbox # Download data for ISS download("https://celestrak.com/NORAD/elements/stations.txt", joinpath(pwd(), "space_stations.txt")) # Initialize the orbit propagator orbp = init_orbit_propagator(Val(:sgp4), read_tle("space_stations.txt")) # Get the current time (Julian date) rightnow = DatetoJD(now()) # Propogate the orbit to "right now" o, r_teme, v_teme = propagate_to_epoch!(orbp, rightnow) # Get the position (radians, radians, meters) lat, lon, h = ECEFtoGeodetic(rECItoECEF(TEME(), ITRF(), rightnow, get_iers_eop())*r_teme) # Nice print out after conversions println("Current location of the ISS: $(rad2deg(lat))° $(rad2deg(lon))° $(h/1000) km")
@mihalybaci Is Santa tracking data available on 24 December?
Not sure, I poked around here a bit, and didn’t see anything for Santa. But this site gets its data from NORAD, and they’re the ones that do the Santa tracking, so it could be hidden in a file somewhere.
Möbius discovered the one-sided non-orientable strip in 1858 while serving as the chair of astronomy at the University of Leipzig. The concept inspired mathematicians in the development of the field of topology as well as artists like M.C. Escher.
Fifteen lines of Julia were required to compute and plot the Mobius strip and a moving normal vector, which changes color after each
2π revolution. This exceeds the limit but someone might be able to compress it further.
(PS: edited code for better readability. Without
sleep, the last
for loop could be written as a comprehension too)
using Makie, ForwardDiff, LinearAlgebra const FDd = ForwardDiff.derivative M(u,v) = ((r + v/2*cos(u/2))*cos(u), (r + v/2*cos(u/2))*sin(u), v/2*sin(u/2)) ∂M∂u(u,v) = [FDd(u->M(u,v),u), FDd(u->M(u,v),u), FDd(u->M(u,v),u)] ∂M∂v(u,v) = [FDd(v->M(u,v),v), FDd(v->M(u,v),v), FDd(v->M(u,v),v)] r = 1.0; w = 0.5; m = 90; clr = (:cyan,:red,:cyan,:red,:cyan) u = range(0, 8π, length = 4m); v = range(-w, w, length = 3) N = [ -cross(∂M∂u(ui, 0.0), ∂M∂v(ui, 0.0))[j] for ui in u, j in 1:3 ] N = N ./ sqrt.(sum(abs2,N,dims=2)); N = vec.(Point3f0.(N[:,1],N[:,2],N[:,3])) xs, ys, zs = [[p[i] for p in M.(u, v')] for i in 1:3] P0 = vec.(Point3f0.(xs[:,2], ys[:,2], zs[:,2])) surface(xs[1:m+1,:], ys[1:m+1,:], zs[1:m+1,:], backgroundcolor=:black) for i in 1:4m sleep(0.01); k = 1 + i÷(m+0.5); arrows!([P0[i]],[N[i]],lengthscale=0.3,arrowsize=0.05,arrowcolor=clr[k],linecolor=clr[k]) end