使用igraph可视化Collat​​z图

Question

我最近研究了Collatz Conjecture，并试图提出一种方法来计算给定数导致1的向量，并一次可视化多个向量。但是，我无法弄清楚如何为图形提供一个好的布局。理想情况下，我想要一个像this或this这样的图形。

这是我的工作

1）计算Collat​​z值的功能

Collatz <- function(x){

    # checking whether the number is a mathematical integer
    if(round(x) != x){

            warning("x must be an integer larger than 1")
            break
    }

    # initializing output vector
    vec <- integer()
    vec[1] <- x

    # checking whether the input is valid
    if(x > 0){

            # continuing computation until we get a 1 in the vector
            while( 1 %in% vec == FALSE){

                    # when the last element of the vector is even
                    if(vec[length(vec)] %% 2 == 0){

                            # initilaize a new element in vec by dividing the previous one by 2
                            vec[length(vec)+1] <- vec[length(vec)]/2

                    }

                    # when the last element of the vector is odd
                    if(vec[length(vec)] %% 2 != 0){

                            # initilaize a new element in vec by multiplying the previous one with 3 and adding 1
                            vec[length(vec)+1] <- 3*vec[length(vec)]+1
                    }

            }   

    } else(warning("x must be an integer larger than 1"))

    # returning output vector except for the last element (which will be 4 insted of 1 due to the while loop)
    return(vec[-length(vec)])
}

2）用于为设定范围内的所有向量创建图形的功能

CollatzGraphing <- function(x){

    # loading igraph library
    library(igraph)

    Numbers <- 1:x
    List <- sapply(Numbers,Collatz)

    # sorting list by length and removing empty lists
    x <- List[order(sapply(List,length),decreasing=T)]
    x <- x[sapply(x,length) >= 2]

    # transforming the vectors into graph format
    x <- lapply(x, rep, each = 2)
    x <- lapply(x, function(y){y[-c(1,length(y))]})
    x <- lapply(x, function(y){as.character(y)})

    # transforming the prepared vectors into graph objects
    x <- lapply(x, graph, directed=TRUE)

    # creating a union of all graph objects
    CompleteGraph <- do.call(union, x)

    # plotting graph
    Plot <- plot(CompleteGraph,
                 vertex.size = 5,
                 edge.arrow.size=.1,
                 vertex.label.cex = 0.5,
                 vertex.color = "white")

    # returning graph object
    return(CompleteGraph)

}

当我在不指定任何布局的情况下使用第二个函数时，会得到如下信息：

Graph1 <- CollatzGraphing(20)

当我尝试使用不同的布局时，图形看起来与我的目标完全不同

V(Graph1)
plot(Graph1,
        vertex.size = 5,
        edge.arrow.size=.1,
        vertex.label.cex = 0.5,
        vertex.color = "white",
        layout = layout_as_tree(Graph1, circular = TRUE, root = 21))

igraph中是否有一种布局可以创建与我一开始所链接的结构相似的结构？