fibonacci

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length_fib = 25
fibonacci = numeric(length_fib)
fibonacci[1] = 1
fibonacci[2] = 1
for (i in 3:length_fib) { 
  fibonacci[i] = fibonacci[i-1] + fibonacci[i-2]
} 

library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.1     ✔ tibble    3.1.8
## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
## ✔ purrr     1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

tibble::tibble(index = 1:length_fib, fibonacci, 
           ydir = rep( c(1, 1, -1, -1), length_fib)[1:length_fib],
           xdir = rep(c(1,-1, -1, 1),length_fib)[1:length_fib],
           ymov = ydir * fibonacci,
           xmov = xdir * fibonacci,
           ypos = cumsum(ymov),
           xpos = cumsum(xmov),
           yprev = lag(ypos),
           xprev = lag(xpos)
           ) %>% 
  mutate(yprev = replace_na(yprev, 0),
         xprev = replace_na(xprev, 0)) %>% 
  slice(1:3) %>% 
  ggplot() + 
  aes(x = xpos, y = ypos) +
  geom_point() + 
  geom_rect(aes(xmin = xprev, xmax = xpos,
                ymin = yprev, ymax = ypos, fill = fibonacci), alpha = .8, color = "white", linewidth = .2) + 
  scale_fill_viridis_c(limits = c(1, 7000), trans = "sqrt") +
  coord_equal(expand = .2)