3D Hadley Attractor

hadley_attractor.R

library(deSolve)
library(rayrender)
parameters = c(a = 0.2, b = 4, c = 8, d = 1)
state = c(X = 1, Y = 0, Z = 1)

Lorenz = function(t, state, parameters) {
  with(as.list(c(state, parameters)), {
    dX = -Y^2 - Z^2 - a*X + a*c
    dY = X * Y - b * X * Z - Y + d
    dZ = b * X * Y + X * Z - Z
    list(c(dX, dY, dZ))
  })
}

times = seq(0, 150, by = 0.1)
vals = ode(y = state, times = times, func = Lorenz, parms = parameters)[,-1]

#scale and rearrange:
meanval = apply(apply(vals,2,range),2,mean)
vals[,1] = vals[,1] - meanval[1]
vals[,2] = vals[,2] - meanval[2]
vals[,3] = vals[,3] - meanval[3]

for(i in 1:360) {
  generate_studio(depth = -2) %>% 
    add_object(path(points = vals,width=0.04,angle=c(0,i,0), 
                    material=glossy(color="red", gradient_color = "dodgerblue4", 
                                     gradient_point_start = c(0,-1.5,0), gradient_point_end = c(0,2,0)))) %>% 
    add_object(sphere(y=5,z=2,material=light(intensity = 40))) %>% 
    render_scene(samples=400,fov=30,clamp_value = 10,width=800,height=800,
                 filename=sprintf("hadleyatt%i.png",i))
}