Thanks Greg and Bert for solving my problem.
This gives what I want:
----------------

myticks <- 2^(3*(0:11))
mylabels <- parse(text=paste0("2^",log2(myticks)))

xyplot(c+t+u~n,data=x,type="b", xlab="Size", ylab="Number of tangles",
  scales=list(x=list(at=4*(1:9)),y=list(log=2,at=myticks,labels=mylabels),
   auto.key=list(columns=3,text=c("(choose m n)","tangles","unique
      tangles"), points=FALSE,lines=TRUE)))
----------------
Solved!
Gerrit

Op 05-09-2024 om 16:54 schreef Bert Gunter:
Do the "at" and "labels" components of the "scales" list argument to xyplot not do what you want?

Cheers,
Bert

On Thu, Sep 5, 2024 at 4:05 AM Gerrit Draisma <gdrai...@xs4all.nl <mailto:gdrai...@xs4all.nl>> wrote:

    Dear R-helpers,

    In the plot below I would like to have labels at positions 2^(3*(0:10)),
    and keep the labels in the exponential format.
    I tried using yscale.components.default.

    *This* gives the right format of the labels:
    --------
      > yscale.components.default(lim= c(0,30),log=2)
    ....
    $num.limit
    [1]  0 30
    ...
    [1]  0  5 10 15 20 25 30
    ...
    $left$labels$labels
    [1] "2^0"  "2^5"  "2^10" "2^15" "2^20" "2^25" "2^30"
    --------

    and *this* gives the right locations
    --------
      > yscale.components.default(lim= c(0,30),log=2,at=2^(3*(0:10)))
    $num.limit
    [1]  0 30
    ...
       [1]  0  3  6  9 12 15 18 21 24 27 30
    ...
    $left$labels$labels
       [1] "1"          "8"          "64"         "512"        "4096"
       [6] "32768"      "262144"     "2097152"    "16777216"   "134217728"
    [11] "1073741824"
    --------

    How can I get the format in the first example at the locations of the
    second?

    Thanks,
    Gerrit

    -------------
    x <- read.csv(text="
    n,c,t,u
    4,1,2,1
    8,28,8,1
    12,495,42,3
    16,8008,256,7
    20,125970,1680,31
    24,1961256,11640,138
    28,30421755,83776,808
    32,471435600,620576,4956
    36,7307872110,4700880,33719")
    library(lattice)
    yscale.components.log2 <- function(...){
          ans <- yscale.components.default(...)
          ans$left$labels$labels <-
              parse(text = ans$left$labels$labels)
          ans
    }


    # pdf("tangle_mathFig06.pdf")
    xyplot(c+t+u~n,data=x,type="b", xlab="Size", ylab="Number of tangles",
         scales=list(x=list(at=4*(1:9)),y=list(log=2)),
         yscale.components=yscale.components.log2,
         auto.key=list(columns=3,text=c("(choose m n)","tangles","unique
    tangles"),
         points=FALSE,lines=TRUE))
    # dev.off()

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