Trends and Triggers Figure
Table of Contents
1 Introduction
This work toward a enhanced figure that might be used to tell a detailed story about the mixture of trend, triggers and wiggles.
2 The History
The original image I base my imagination on is:
- Scheffer, M., & Carpenter, S. R. (2003). Catastrophic regime shifts in ecosystems: linking theory to observation [Review]. TRENDS in Ecology and Evolution, 18(12), 648–656. Retrieved from http://eaton.math.rpi.edu/csums/papers/Ecostability/scheffercatastrophe.pdf
Which was based on
- Scheffer, M., Carpenter, S., Foley, J. a, Folke, C., & Walker, B. (2001). Catastrophic shifts in ecosystems. Nature, 413(6856), 591–6. <doi:10.1038/35098000>
3 3D surface
First I want to generate a 3d computer image to play with perspective and shading.
3.1 figure
3.2 code
#### name:generate-surface #### x <- seq(from=-2.5, to=2.5, by=0.1) zid <- .1 for(y in 1:10) { z <- x^4 - zid * x^3 - 7 * x^2 + x + 6 if(y == 1) { data_out <- cbind(x,y,z) } else { data_out <- rbind(data_out, cbind(x,y,z)) } zid <- zid + 0.1 } data_out <- as.data.frame(data_out) write.csv(data_out, "TrendsAndTriggers-v2.csv", row.names = F) png("/images/TrendsAndTriggers-v2.png") persp(x, 1:10, matrix(data_out$z, ncol = 10, nrow = length(x)), ylab= "", xlab= "", zlab = "", theta = 140, phi = 42, expand = 0.5, col = "lightgrey") dev.off()
4 Try an animation
I'd like to move the ball through the surface. First need to calculate the path.
4.1 figure
4.2 code
# functions if(!require(animation)) install.packages("animation"); require(animation) # load data_out <- read.csv("TrendsAndTriggers-v2.csv") ## do setwd("images") saveGIF( { ani.options(interval = 0.2) xindex <- c(0, -1, rep(-1.9, 6), -1, 0, 1, rep(2, 6), 1, 0 , 0) j <- 1 xind <- xindex[j] for(index in c(1:10, 9:1)){ with(subset(data_out, y == index), plot(x, z, type = "l", ylim = c(-15,15)) ) with(subset(data_out, y == index & x == xind), points(x,z,pch=16,cex = 3) ) j <- j + 1 xind <- xindex[j] } }, outdir = getwd() ) setwd("..")
5 Next Steps
- the polynomials should move up and down to give the height of originals
- the hump in the middle needs to change, so the ball flips more easily
- I'd like the ball to wiggle, add a random walk
- the time series dimension needs to be shown
- It'd be great to combine this with 2D line plots as well
