Latest posts tagged with #MathViz on Bluesky
Orthographic projection gives you the "globe photo" look; parallel rays, no angle distortion at center.
But what happens at the edges? That's where things get interesting.
Both projections side-by-side in the article ⬇️
ideable.dev/starplot/03-...
#CodingTutorial #MathViz #JavaScript
🧪 What if odd integers behaved like light beams? I built a "Collatz Interferometer" to find out.
My new app splits odd integers into components (2n, 2n+1) to test if the math stays linear during a collatz operation.
🔗 prayogashaala.com/the-collatz-... #MathViz #Physics #NumberTheory
Overview: Hacker News debated "fuzzy graphing," a new approach visualizing the difference between equation sides, not just solutions. Author claimed novelty, but many saw it as existing techniques like heatmaps. Discussion explored its utility & mathematical ties. #MathViz 1/6
![The entire code lorenz.jl:
using CUDA
using StaticArrays
using Plots
using DifferentialEquations
@kwdef struct AttractorParams
σ::Float64 = 10.0
ρ::Float64 = 28.0
β::Float64 = (8.0 / 3.0)
end
function lorenz!(du, u, params, _)
x, y, z = u
du[1] = params.σ * (y - x)
du[2] = x * (params.ρ - z) - y
du[3] = (x * y) - (params.β * z)
return nothing
end
function simulate(initial_condition, tspan, params)
prob = ODEProblem(lorenz!, initial_condition, tspan, params)
return solve(prob, Tsit5(), reltol=1e-6, abstol=1e-6)
end
function plot_xz(sol)
x_coords = [point[1] for point in sol.u]
z_coords = [point[3] for point in sol.u]
p = plot(x_coords, z_coords, seriestype=:path, xlabel="X", ylabel="Z", lw=0.25, alpha=07, size=(1200, 1200))
return p
end
function plot_xy(sol)
x_coords = [point[1] for point in sol.u]
y_coords = [point[2] for point in sol.u]
p = plot(x_coords, y_coords, seriestype=:path, xlabel="X", ylabel="Y", lw=0.5, alpha=0.7, size=(1200, 1200),
background_color=:black, legend=false, linecolor=cgrad(:viridis))
return p
end
function run_sim()
u0 = [1.0, 0.0, 0.0]
tspan = (0.0, 1000.0)
sim_results = simulate(u0, tspan, AttractorParams())
viz = plot_xy(sim_results)
display(viz)
end](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:s5zwyygnkcdgblepvwused47/bafkreib2pojuqvkgeiovgpsbntkpg57xpxmypa573psz5l5vwobb4rxzyi)
The entire code lorenz.jl: using CUDA using StaticArrays using Plots using DifferentialEquations @kwdef struct AttractorParams σ::Float64 = 10.0 ρ::Float64 = 28.0 β::Float64 = (8.0 / 3.0) end function lorenz!(du, u, params, _) x, y, z = u du[1] = params.σ * (y - x) du[2] = x * (params.ρ - z) - y du[3] = (x * y) - (params.β * z) return nothing end function simulate(initial_condition, tspan, params) prob = ODEProblem(lorenz!, initial_condition, tspan, params) return solve(prob, Tsit5(), reltol=1e-6, abstol=1e-6) end function plot_xz(sol) x_coords = [point[1] for point in sol.u] z_coords = [point[3] for point in sol.u] p = plot(x_coords, z_coords, seriestype=:path, xlabel="X", ylabel="Z", lw=0.25, alpha=07, size=(1200, 1200)) return p end function plot_xy(sol) x_coords = [point[1] for point in sol.u] y_coords = [point[2] for point in sol.u] p = plot(x_coords, y_coords, seriestype=:path, xlabel="X", ylabel="Y", lw=0.5, alpha=0.7, size=(1200, 1200), background_color=:black, legend=false, linecolor=cgrad(:viridis)) return p end function run_sim() u0 = [1.0, 0.0, 0.0] tspan = (0.0, 1000.0) sim_results = simulate(u0, tspan, AttractorParams()) viz = plot_xy(sim_results) display(viz) end
A visualization of the XY projection of the classic Lorenz System.
So it turns out that in Julia if you want to render a the Lorenz system efficiently, you don't have to manually integrate it via iteration, there's this library with ODE system support that automatically uses CUDA if you load it. The code for this was fast. (h/t @ponder.ooo )
#julia #mathviz
