georgemsavva

# Hilbert curve in R

# Make some matrices to do rotation and flip
rotmat = function(theta) matrix(c(cos(theta),-sin(theta),sin(theta), cos(theta)),nrow=2)
rotclock = rotmat(pi/2)
rotaclock = rotmat(-pi/2)
flip=matrix(c(-1,0,0,1),nrow=2)
ident=matrix(c(1,0,0,1),nrow=2)

# Define the recursive function to generate the points in the right order

georgemsavva

N=42
ratio=0.8
t = seq(1,N/2*pi,l=100000)
stepper = .5*(2*((t%%pi)/pi-0.5))^5 + (t%/%pi)
circle = function(a,p,f) {
  exp(1i*(t*f + p + 0*t/N*.5))*a
  }
w=1000
Nf=N/6
drawchar = function(x,y,width,height,a=1,p,f,...){

georgemsavva

par(mfrow=c(1,1))
par(mar=c(0,0,0,0))
l=1.2
# variables
res=2000
n=1000
x <- y <- seq(-l,l, length.out=res)
c <- outer(x,y*1i,FUN="+")
z <- matrix(0.0, nrow=res, ncol=res)
o <- matrix(1e5, nrow=res, ncol=res)

georgemsavva

par(mfrow=c(1,1))
par(mar=c(0,0,0,0))
l=1.2
# variables
res=1000
n=500
x <- y <- seq(-l,l, length.out=res)
c <- outer(x,y*1i,FUN="+")
z <- matrix(0.0, nrow=res, ncol=res)
o <- matrix(1e5, nrow=res, ncol=res)

georgemsavva

# There is some explanation for why the bitwise operator functions do what they do here:
# https://inventwithpython.com/blog/2021/08/02/algorithmic-art-with-the-bitfielddraw-module/

# ignore the warnings, THIS IS ART!


library(ggplot2)

cols <- c("#b8e1c5", "#3ac9fb", "#fadacc","#fcb2c6", 
          "#002f88", "#fd7a5d","#00B850", "#091a22")

georgemsavva

# There is some explanation for why the bitwise operator functions do what they do here:
# https://inventwithpython.com/blog/2021/08/02/algorithmic-art-with-the-bitfielddraw-module/

# for the colour palettes
library(RColorBrewer) 

# Set the aspect ratio
ratio = 5/4

# How many images do we want

georgemsavva

library(magick)

# This is the function for the basic shape
flower <- function(a){
  # make an index
  t <- seq(0,202,l=499)
  # make a curve
  z1 <- (1i*(1i^a)*cos(2*t*pi)*(1) + 1*(1i^a)*(sin(2*t*pi))*(1) )
  # modulate the curve
  z1*(3+(sin(a*Arg(z1))*cos(a*Arg(z1))*cos((10-a)*Arg(z1))))

georgemsavva

# The formula to iterate
logisticMap <- function(x, r) r * x * (1-x)

# Iterate N times from starting point
makeMap <- function(x , r, N){
  for(i in 2:N) x[i] <- logisticMap(x[i-1], r)
  x
}

# How many iterations?

georgemsavva

# Code to generate Bezier 'mesh' images inspired by the work of Jacquie Tran (https://art.jacquietran.com/)

# Function to calculate Bezier curves
bezierz <- function(z1,z2,ct,ct2,ct3,l,o=2){
  ll=1-l
  if(o==3) return(z1*ll^4 + 4*ct*ll^3*l + 6*ct2*ll^2*l^2 + 4*ct3*ll*l^3 + z2*l^4)
  if(o==2) return(z1*ll^3 + 3*ct*ll^2*l + 3*ct2*ll*l^2 + z2*l^3)
  if(o==1) return(z1*ll^2 + 2*ct*ll*l + z2*l^2)
}

georgemsavva

# Set random number seed for reproducibility
set.seed(2210)

# Number of starting points
N=5000

# Describe the flow function
flow <- function(z,bs) {    
    fz <- ((z+bs[1])*(z+bs[2])*(z+bs[3])*(z+bs[4])*(z+bs[8]))/
          ((z+bs[5])*(z+bs[6])*(z+bs[7]))