I want the function do the same job like **ReplaceRepeated**,and can make the symbol become visibleness.
I search the Internet and don't find any package.So I write one...

 Clear[myReplaceRepeated];
 myReplaceRepeated[lis_List, rule_, n_: Infinity] := 
 Module[{variables, mat = rule[[1]], data, tem}, 
 variables = 
 ToExpression@
 StringCases[
 ToString[mat], (vars : WordCharacter ..) ~~ "_" | "__" | "___" :> vars];
 If[variables != {},
 
 testQ = Table[Cases[#1, #2 -> i, {0}], {i, variables}] &;
 data = 
 Reap[FixedPointList[(Sow[testQ[#, mat]]; # /. rule) &, lis, 
 n]][[2, 1]]; 
 Labeled[Grid[Prepend[data, variables], Frame -> All, 
 Background -> {Lighter /@ 
 Hue /@ Range[0, 1, 1/Length[variables]]}], 
 Column[{lis, "the rule is", rule}], Top],
 
 Labeled[
 Grid[tem = Most@FixedPointList[# /. rule &, lis, n], Frame -> All,
 Background -> {None, {Lighter /@ 
 Hue /@ Range[0, 1, 1/Length[tem]]}}], 
 Column[{lis, "the rule is", rule}], Top]
 ]]

So I can test some example in **ReplaceRepeated**

example 1:

 myReplaceRepeated[{1, 3, 1, 4, 1, 3, 4, 2, 7, 1, 8}, 
 {Longest[a___], b_, c__, b_, d___} -> {b, b, a, c, d}]

![enter image description here][1]

example 2:

 myReplaceRepeated[{1, a, 2, b, 3, c}, _?NumericQ -> F[Infinity], 4](*4 is set the MaxIterations*)
 
![From "Mathematica Cookbook"][2]

example 3:

 myReplaceRepeated[{1, 2}, {a_, b_} -> {{a}, {b}}, 5]](*5 is also set the MaxIterations*)

![From "Mathematica Cookbook"][3]

But some example fails,for example:
 
 myReplaceRepeated[f[a][b][c][d], g_[x_][y__] -> g[x, y]]
 myReplaceRepeated[Log[Sqrt[a (b c^d)^e]], {Log[x_ y_] :> Log[x] + Log[y], Log[x_^k_] :> k Log[x]}]

So I want to know how to improve my Program？ 
If there is a tool can make Pattern Matching become visualization?

***Edit:***

I will explain my function more carefully and I want to use this example.

First,define two things,one is the *expr* and the other is *rule*

 lis = {1, 3, 1, 4, 1, 3, 4, 2, 7, 1, 8};
 rule = {Longest[a___], b_, c__, b_, d___} -> {b, b, a, c, d};
 mat(*means match*) = rule[[1]]

> {Longest[a___], b_, c__, b_, d___}

And then, I want to know the a,b,c and d in "mat" how to represent the sub-list in "lis"?
but how many varibles in rule? So I must find these variables...

 variables = 
 ToExpression@StringCases[
 ToString[mat], (vars : WordCharacter ..) ~~ "_" | "__" | "___" :> vars]

> {a, b, c, b, d}

Ok,Next~ This code means "a" represent {1,3,1,4} in lis.
**But remember,the level is {0},otherwise we gets {}**

 Cases[{1, 3, 1, 4, 1, 3, 4, 2, 7, 1, 
 8}, {Longest[a___], b_, c__, b_, d___} -> a, {0}]

> {1, 3, 1, 4}

Ok,combine these in a loop.

 Table[Cases[{1, 3, 1, 4, 1, 3, 4, 2, 7, 1, 
 8}, {Longest[a___], b_, c__, b_, d___} -> i, {0}], {i, variables}]

> {{1, 3, 1, 4}, {1}, {3, 4, 2, 7}, {1}, {8}}

the output means "a" represent {1,3,1,4},"b" represent {1},"c" represent {3,4,2,7},the next "b" means the forth {1} and the "d" represent {8} in "lis".

Ok,Combine these together and use pure function to illustrate **testQ**

 testQ = Module[{variables}, 
 variables = 
 ToExpression@
 StringCases[
 ToString[#2], (vars : WordCharacter ..) ~~ 
 "_" | "__" | "___" :> vars];
 Table[Cases[#1, #2 -> i, {0}], {i, variables}]] &;
 testQ[lis, mat]

> {{1, 3, 1, 4}, {1}, {3, 4, 2, 7}, {1}, {8}}

Ok.**ReplaceRepeated** function can be overwriten by **FixedPointList**.The process of FixedPointList can bring a side effect that is always search the a,b,c,d represent what sub-list..

 data = Reap[
 FixedPointList[(Sow[
 testQ[#, 
 mat]]; # /. {Longest[a___], b_, c__, b_, d___} -> {b, b, a, c,
 d}) &, {1, 3, 1, 4, 1, 3, 4, 2, 7, 1, 8}]][[2, 1]];
 Grid@data

> ![enter image description here][4]

Finally,we get the similar result.

 [1]: https://i.sstatic.net/VCnMC.png
 [2]: https://i.sstatic.net/dXby5.png
 [3]: https://i.sstatic.net/9gzwN.png
 [4]: https://i.sstatic.net/US0vv.png