第一篇随笔，先写点简单的。初学OCaml请大家多多包涵，多提意见。

　　这篇文章实现一个最简单的分型--递归二叉树。当然这个分型是有限的，并没有制造它的无限放大模式。

　　首先构造递归二叉树的最小递归单元。

　　

　　整个递归树就是在树叉部分不停的迭代这个结构制作成的。

　　现在分别是以当前点(current_point)位基准点,当前角度(current_angle )为基准角度计算一定长度(length)一定角度(angle)左子树和右子树定位的位置。

左子树：

(*float -> int -> float -> int * int = int * int*) let left angle length current_angle current_point=

let x = round ((sin (angle +. current_angle)) *. float_of_int length) + (fst current_point)         and y = round ((cos (angle +. current_angle)) *. float_of_int length) + (snd current_point)         in (x, y)

右子树：

　　

(*float -> int -> float -> int * int = int * int*) let right angle length current_angle current_point=         let x = round ((sin (current_angle -. angle)) *. float_of_int length) + (fst current_point)        and y = round ((cos (current_angle -. angle)) *. float_of_int length) + (snd current_point)        in (x, y)

其中：round函数式做四舍五入的，因为OCaml没有提供四舍五入的函数,自己动手实现

(*    制造一个四舍五入的函数，    Ocaml并没有提供四舍五入的函数，    所以利用OCaml提供的    ceil float -> float函数    floor float -> float函数    构造四舍五入函数    round float -> int*)let round x =                                         let decimals = x -. (float_of_int (truncate x)) in    match decimals with    | 0. -> int_of_float x    | d when d >= 0.5 -> int_of_float (ceil x)    | d -> int_of_float (floor x);;

递归的画整个树，并且还为整个树的每个层级分配一个颜色。以下是画树的代码

(*画树：    树的参数为左右张开的角度，angle    树的层次，由num step构成，num为第一层的高，step每层得递减高度    起始颜色：col代表起始颜色 大小是一个0 ~ 255*255*255的数字*)let draw_tree angle num step col =    let colorstep = (255 * 255 * 255 - col ) /  (num / step) in    let convert_color col_int = Graphics.rgb (col_int mod (255 * 255)) (col_int / 255 mod 255) (col_int mod 255) in     let left angle length current_angle current_point=         let x = round ((sin (angle +. current_angle)) *. float_of_int length) + (fst current_point)        and y = round ((cos (angle +. current_angle)) *. float_of_int length) + (snd current_point)        in (x, y)    and right angle length current_angle current_point=         let x = round ((sin (current_angle -. angle)) *. float_of_int length) + (fst current_point)        and y = round ((cos (current_angle -. angle)) *. float_of_int length) + (snd current_point)        in (x, y)    in     let rec draw_subtree current_angle n innercol=             match n with            | n when n <= 0 -> ();            | n ->                 let current_point = Graphics.current_point () in                let left_point = left angle n current_angle current_point in                 let right_point = right angle n current_angle current_point in                Graphics.set_color (convert_color innercol) ;                Graphics.lineto (fst left_point) (snd left_point);                draw_subtree (current_angle +. angle) (n - step) (innercol + colorstep);                Graphics.moveto (fst current_point) (snd current_point);                Graphics.set_color (convert_color innercol) ;                Graphics.lineto (fst right_point) (snd right_point);                draw_subtree (current_angle -. angle) (n - step) (innercol + colorstep);    in draw_subtree 0. num col;;

完事具备，剩下的事情就是初始化系统环境，并画一棵树。

#load "graphics.cma";;                (*加载OCaml图形库*)Graphics.open_graph "";;            (*打开窗口*)Graphics.set_window_title "recursion_tree";; (*设置窗口标题*)

(*移动到图像中央*)Graphics.moveto 500 0 ;;(*画一棵树，角度为0.2，一层高度为45 每阶递减3 初始颜色 255 * 255*)draw_tree 0.2 45 3 (1 * 255 * 255);;

最终一颗递归树形成了：

以下为完整代码：

　　

#load "graphics.cma";;                (*加载OCaml图形库*)Graphics.open_graph "";;            (*打开窗口*)Graphics.set_window_title "recursion_tree";; (*设置窗口标题*)(*    制造一个四舍五入的函数，    Ocaml并没有提供四舍五入的函数，    所以利用OCaml提供的    ceil float -> float函数    floor float -> float函数    构造四舍五入函数    round float -> int*)let round x =                                         let decimals = x -. (float_of_int (truncate x)) in    match decimals with    | 0. -> int_of_float x    | d when d >= 0.5 -> int_of_float (ceil x)    | d -> int_of_float (floor x);; (*画树：    树的参数为左右张开的角度，angle    树的层次，由num step构成，num为第一层的高，step每层得递减高度    起始颜色：col代表起始颜色 大小是一个0 ~ 255*255*255的数字*)let draw_tree angle num step col =    let colorstep = (255 * 255 * 255 - col ) /  (num / step) in    let convert_color col_int = Graphics.rgb (col_int mod (255 * 255)) (col_int / 255 mod 255) (col_int mod 255) in     let left angle length current_angle current_point=         let x = round ((sin (angle +. current_angle)) *. float_of_int length) + (fst current_point)        and y = round ((cos (angle +. current_angle)) *. float_of_int length) + (snd current_point)        in (x, y)    and right angle length current_angle current_point=         let x = round ((sin (current_angle -. angle)) *. float_of_int length) + (fst current_point)        and y = round ((cos (current_angle -. angle)) *. float_of_int length) + (snd current_point)        in (x, y)    in     let rec draw_subtree current_angle n innercol=             match n with            | n when n <= 0 -> ();            | n ->                 let current_point = Graphics.current_point () in                let left_point = left angle n current_angle current_point in                 let right_point = right angle n current_angle current_point in                Graphics.set_color (convert_color innercol) ;                Graphics.lineto (fst left_point) (snd left_point);                draw_subtree (current_angle +. angle) (n - step) (innercol + colorstep);                Graphics.moveto (fst current_point) (snd current_point);                Graphics.set_color (convert_color innercol) ;                Graphics.lineto (fst right_point) (snd right_point);                draw_subtree (current_angle -. angle) (n - step) (innercol + colorstep);    in draw_subtree 0. num col;;(*移动到图像中央*)Graphics.moveto 500 0 ;;(*画一棵树，角度为0.2，一层高度为45 每阶递减3 初始颜色 255 * 255*)draw_tree 0.2 45 3 (1 * 255 * 255);;