⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

;Task: Create a [http://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence Thue-Morse sequence].

• YouTube entry: [https://www.youtube.com/watch?v=Tt5TTid6YXk Math and OCD - My story with the Thue-Morse sequence]

Implementation using an L-system.

```with Ada.Text_IO; use Ada.Text_IO;

procedure Thue_Morse is

function Replace(S: String) return String is
-- replace every "0" by "01" and every "1" by "10"
(if S'Length = 0 then ""
else (if S(S'First) = '0' then "01" else "10") &
Replace(S(S'First+1 .. S'Last)));

function Sequence (N: Natural) return String is
(if N=0 then "0" else Replace(Sequence(N-1)));

begin
for I in 0 .. 6 loop
Ada.Text_IO.Put_Line(Integer'Image(I) & ": " & Sequence(I));
end loop;
end Thue_Morse;
```

{{out}}

``` 0: 0
1: 01
2: 0110
3: 01101001
4: 0110100110010110
5: 01101001100101101001011001101001
6: 0110100110010110100101100110100110010110011010010110100110010110
```

## ALGOL 68

```# "flips" the "bits" in a string (assumed to contain only "0" and "1" characters) #
OP  FLIP = ( STRING s )STRING:
BEGIN
STRING result := s;
FOR char pos FROM LWB result TO UPB result DO
result[ char pos ] := IF result[ char pos ] = "0" THEN "1" ELSE "0" FI
OD;
result
END; # FLIP #

# print the first few members of the Thue-Morse sequence #
STRING tm := "0";
TO 7 DO
print( ( tm, newline ) );
tm +:= FLIP tm
OD
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## AppleScript

{{Trans|JavaScript}}

```-- THUE MORSE ----------------------------------------------------------------

-- thueMorse :: Int -> String
on thueMorse(nCycles)
script concatBinaryInverse
on |λ|(xs)
script binaryInverse
on |λ|(x)
1 - x
end |λ|
end script

xs & map(binaryInverse, xs)
end |λ|
end script

intercalate("", ¬
foldl(concatBinaryInverse, [0], enumFromTo(1, nCycles)))
end thueMorse

-- TEST ----------------------------------------------------------------------
on run

thueMorse(6)

--> 0110100110010110100101100110100110010110011010010110100110010110
end run

-- GENERIC LIBRARY FUNCTIONS

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- intercalate :: Text -> [Text] -> Text
on intercalate(strText, lstText)
set {dlm, my text item delimiters} to {my text item delimiters, strText}
set strJoined to lstText as text
set my text item delimiters to dlm
return strJoined
end intercalate

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
```
```"0110100110010110100101100110100110010110011010010110100110010110"
```

## AWK

```BEGIN{print x="0"}
{gsub(/./," &",x);gsub(/ 0/,"01",x);gsub(/ 1/,"10",x);print x}
```

=

## BASIC256

= {{trans|FreeBASIC}}

```
tm = "0"

Function Thue_Morse(s)
k = ""
For i = 1 To Length(s)
If Mid(s, i, 1) = "1" Then
k += "0"
Else
k += "1"
End If
Next i
Thue_Morse = s + k
End Function

Print tm
For j = 1 To 7
tm = Thue_Morse(tm)
Print tm
Next j
End

```

{{out}}

```
Igual que la entrada de FreeBASIC.

```

=

## Sinclair ZX81 BASIC

=

``` 10 LET T\$="0"
20 PRINT "T0=";T\$
30 FOR I=1 TO 7
40 PRINT "T";I;"=";
50 FOR J=1 TO LEN T\$
60 IF T\$(J)="0" THEN GOTO 90
70 LET T\$=T\$+"0"
80 GOTO 100
90 LET T\$=T\$+"1"
100 NEXT J
110 PRINT T\$
120 NEXT I
```

{{out}}

```T0=0
T1=01
T2=0110
T3=01101001
T4=0110100110010110
T5=01101001100101101001011001101001
T6=0110100110010110100101100110100110010110011010010110100110010110
T7=01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001
```

## BBC BASIC

```thuemorse
tm\$ = "0"
PRINT tm\$
FOR i% = 1 TO 8
tm\$ = FN_thue_morse(tm\$)
PRINT tm\$
NEXT
END
:
DEF FN_thue_morse(previous\$)
LOCAL i%, tm\$
tm\$ = ""
FOR i% = 1 TO LEN previous\$
IF MID\$(previous\$, i%, 1) = "1" THEN tm\$ += "0" ELSE tm\$ += "1"
NEXT
= previous\$ + tm\$
```

{{out}}

```0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110
```

## Befunge

{{trans|C}}

This implements the algorithm that counts the 1 bits in the binary representation of the sequence number.

```:0\:!v!:\+g20\<>*:*-!#@_
86%2\$_:2%02p2/^^82:+1,+*
```

{{out}}

```0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110
```

## C

### C: Using string operations

{{trans|Java}}

```#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(int argc, char *argv[]){
char sequence[256+1] = "0";
char inverse[256+1] = "1";
char buffer[256+1];
int i;

for(i = 0; i < 8; i++){
strcpy(buffer, sequence);
strcat(sequence, inverse);
strcat(inverse, buffer);
}

puts(sequence);
return 0;
}
```

{{out}}

```
0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110

```

### C: By counting ones in binary representation of an iterator

```#include <stdio.h>

/**
* description : Counts the number of bits set to 1
*        input: the number to have its bit counted
*       output: the number of bits set to 1
*/
unsigned count_bits(unsigned v) {
unsigned c = 0;
while (v) {
c += v & 1;
v >>= 1;
}

return c;
}

int main(void) {
for (unsigned i = 0; i < 256; ++i) {
putchar('0' + count_bits(i) % 2);
}
putchar('\n');

return 0;
}
```

{{out}}

```
0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110

```

===C: By counting ones in binary representation of an iterator (w/User options)===

```

/**
* description : Counts the number of bits set to 1
*        input: the number to have its bit counted
*       output: the number of bits set to 1
*/
unsigned count_bits(unsigned v) {
unsigned c = 0;
while (v) {
c += v & 1;
v >>= 1;
}

return c;
}

int main(void) {
/*          i: loop iterator
*     length: the length of the sequence to be printed
* ascii_base: the lower char for use when printing
*/
unsigned i, length = 0;
int ascii_base;

/* scan in sequence length */
printf("Sequence length: ");
do {
scanf("%u", &length);
} while (length == 0);

/* scan in sequence mode */
printf("(a)lpha or (b)inary: ");
do {
ascii_base = getchar();
} while ((ascii_base != 'a') && (ascii_base != 'b'));
ascii_base = ascii_base == 'b' ? '0' : 'A';

/* print the Thue-Morse sequence */
for (i = 0; i < length; ++i) {
putchar(ascii_base + count_bits(i) % 2);
}
putchar('\n');

return 0;
}
```

{{out}}

```
Sequence length: 256
(a)lpha or (b)inary: b
0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110

```

## C++

```
#include <iostream>
#include <iterator>
#include <vector>
int main( int argc, char* argv[] ) {
std::vector<bool> t;
t.push_back( 0 );
size_t len = 1;
std::cout << t[0] << "\n";
do {
for( size_t x = 0; x < len; x++ )
t.push_back( t[x] ? 0 : 1 );
std::copy( t.begin(), t.end(), std::ostream_iterator<bool>( std::cout ) );
std::cout << "\n";
len = t.size();
} while( len < 60 );
return 0;
}

```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## C#

{{trans|Java}}

```using System;
using System.Text;

namespace ThueMorse
{
class Program
{
static void Main(string[] args)
{
Sequence(6);
}

public static void Sequence(int steps)
{
var sb1 = new StringBuilder("0");
var sb2 = new StringBuilder("1");
for (int i = 0; i < steps; i++)
{
var tmp = sb1.ToString();
sb1.Append(sb2);
sb2.Append(tmp);
}
Console.WriteLine(sb1);
}
}
}
```
```0110100110010110100101100110100110010110011010010110100110010110
```

## Common Lisp

```(defun bit-complement (bit-vector)
(loop with result = (make-array (length bit-vector) :element-type 'bit)
for b across bit-vector
for i from 0
do (setf (aref result i) (- 1 b))
finally (return result)))

(defun next (bit-vector)
(concatenate 'bit-vector bit-vector (bit-complement bit-vector)))

(defun print-bit-vector (bit-vector)
(loop for b across bit-vector
do (princ b)
finally (terpri)))

(defun thue-morse (max)
(loop repeat (1+ max)
for value = #*0 then (next value)
do (print-bit-vector value)))

(thue-morse 6)
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## D

{{trans|C}}

```import std.range;
import std.stdio;

struct TM {
private char[] sequence = ['0'];
private char[] inverse = ['1'];
private char[] buffer;

enum empty = false;

auto front() {
return sequence;
}

auto popFront() {
buffer = sequence;
sequence ~= inverse;
inverse ~= buffer;
}
}

void main() {
TM sequence;

foreach (step; sequence.take(8)) {
writeln(step);
}
}

```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Elena

{{trans|C#}} ELENA 4.x :

```import extensions;
import system'text;

sequence(int steps)
{
for(int i := 0, i < steps, i += 1)
{
var tmp := sb1.Value;
sb1.write(sb2);
sb2.write(tmp)
};
}

public program()
{
sequence(6)
}
```

{{out}}

```
0110100110010110100101100110100110010110011010010110100110010110

```

## Elixir

```Enum.reduce(0..6, '0', fn _,s ->
IO.puts s
s ++ Enum.map(s, fn c -> if c==?0, do: ?1, else: ?0 end)
end)

# or
Stream.iterate('0', fn s -> s ++ Enum.map(s, fn c -> if c==?0, do: ?1, else: ?0 end) end)
|> Enum.take(7)
|> Enum.each(&IO.puts/1)
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Factor

{{works with|Factor|0.98}}

```USING: io kernel math math.parser sequences ;

: thue-morse ( seq n -- seq' )
[ [ ] [ [ 1 bitxor ] map ] bi append ] times ;

: print-tm ( seq -- ) [ number>string ] map "" join print ;

7 <iota> [ { 0 } swap thue-morse print-tm ] each
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Fortran

{{works with|Fortran|90 and later}}

```program thue_morse
implicit none
logical :: f(32) = .false.
integer :: n = 1

do
write(*,*) f(1:n)
if (n > size(f)/2) exit
f(n+1:2*n) = .not. f(1:n)
n = n * 2
end do

end program thue_morse
```

{{out}}

```
F
F  T
F  T  T  F
F  T  T  F  T  F  F  T
F  T  T  F  T  F  F  T  T  F  F  T  F  T  T  F
F  T  T  F  T  F  F  T  T  F  F  T  F  T  T  F  T  F  F  T  F  T  T  F  F  T  T  F  T  F  F  T

```

## FreeBASIC

```
Dim As String tm = "0"

Function Thue_Morse(s As String) As String
Dim As String k = ""
For i As Integer = 1 To Len(s)
If Mid(s, i, 1) = "1" Then
k += "0"
Else
k += "1"
End If
Next i
Thue_Morse = s + k
End Function

Print tm
For j As Integer = 1 To 7
tm = Thue_Morse(tm)
Print tm
Next j
End

```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001

```

## Go

```// prints the first few members of the Thue-Morse sequence

package main

import (
"fmt"
"bytes"
)

// sets tmBuffer to the next member of the Thue-Morse sequence
// tmBuffer must contain a valid Thue-Morse sequence member before the call
func nextTMSequenceMember( tmBuffer * bytes.Buffer ) {
// "flip" the bytes, adding them to the buffer
for b, currLength, currBytes := 0, tmBuffer.Len(), tmBuffer.Bytes() ; b < currLength; b ++ {
if currBytes[ b ] == '1' {
tmBuffer.WriteByte( '0' )
} else {
tmBuffer.WriteByte( '1' )
}
}
}

func main() {
var tmBuffer bytes.Buffer
// initial sequence member is "0"
tmBuffer.WriteByte( '0' )
fmt.Println( tmBuffer.String() )
for i := 2; i <= 7; i ++ {
nextTMSequenceMember( & tmBuffer )
fmt.Println( tmBuffer.String() )
}
}
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

Computing progressively longer prefixes of the sequence,

```import Control.Monad

thueMorsePxs = ap (++) (map (1-)) `iterate` [0]
{-
= iterate ((++) <*> map (1-)) [0]
= iterate (\ xs -> (++) xs (map (1-) xs)) [0]
= iterate (\ xs -> xs ++ map (1-) xs) [0]
-}
```

'''Output:'''

```~> thueMorsePxs !! 5
[0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1]
```

The infinite sequence itself:

```thueMorse = [0] ++ g 1
where
g i = map (1-) (take i thueMorse) ++ g (i*2)
```

'''Output:'''

```~> take 33 thueMorse
[0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,1]
```

## J

We only show a prefix of the sequence:

```   (, -.)@]^:[&0]9
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 ...
```

Or, more compactly:

```   ' '-.~":(, -.)@]^:[&0]9
0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110...
```

## Java

```public class ThueMorse {

public static void main(String[] args) {
sequence(6);
}

public static void sequence(int steps) {
StringBuilder sb1 = new StringBuilder("0");
StringBuilder sb2 = new StringBuilder("1");
for (int i = 0; i < steps; i++) {
String tmp = sb1.toString();
sb1.append(sb2);
sb2.append(tmp);
}
System.out.println(sb1);
}
}
```
```0110100110010110100101100110100110010110011010010110100110010110
```

## Julia

{{works with|Julia|0.6}}

```function thuemorse(len::Int)
rst = Vector{Int8}(len)
rst[1] = 0
i, imax = 2, 1
while i ≤ len
while i ≤ len && i ≤ 2 * imax
rst[i] = 1 - rst[i-imax]
i += 1
end
imax *= 2
end
return rst
end

println(join(thuemorse(100)))
```

{{out}}

```0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110
```

## Kotlin

{{trans|Java}}

```// version 1.1.2
fun thueMorse(n: Int): String {
val sb0 = StringBuilder("0")
val sb1 = StringBuilder("1")
(0 until n).forEach {
val tmp = sb0.toString()
sb0.append(sb1)
sb1.append(tmp)
}
return sb0.toString()
}

fun main(args: Array<String>) {
for (i in 0..6) println("\$i : \${thueMorse(i)}")
}
```

{{out}}

```
0 : 0
1 : 01
2 : 0110
3 : 01101001
4 : 0110100110010110
5 : 01101001100101101001011001101001
6 : 0110100110010110100101100110100110010110011010010110100110010110

```

## JavaScript

### ES5

{{trans|Java}}

```(function(steps) {
'use strict';
var i, tmp, s1 = '0', s2 = '1';
for (i = 0; i < steps; i++) {
tmp = s1;
s1 += s2;
s2 += tmp;
}
console.log(s1);
})(6);
```
```0110100110010110100101100110100110010110011010010110100110010110
```

### ES6

```(() => {
'use strict';

// THUE MORSE

// thueMorse :: Int -> String
let thueMorse = nCycles => range(1, Math.abs(nCycles))
.reduce(a => a.concat(a.map(x => 1 - x)), [0])
.join('');

// GENERIC FUNCTION

// range :: Int -> Int  -> [Int]
let range = (m, n) => Array.from({
length: Math.floor((n - m)) + 1
}, (_, i) => m + i);

// TEST

return thueMorse(6);

// 0110100110010110100101100110100110010110011010010110100110010110

})();

```

{{Out}}

```0110100110010110100101100110100110010110011010010110100110010110
```

## Lua

```ThueMorse = {sequence = "0"}

function ThueMorse:show ()
print(self.sequence)
end

local newBlock = ""
for bit = 1, self.sequence:len() do
if self.sequence:sub(bit, bit) == "1" then
newBlock = newBlock .. "0"
else
newBlock = newBlock .. "1"
end
end
self.sequence = self.sequence .. newBlock
end

for i = 1, 5 do
ThueMorse:show()
end
```

{{out}}

```0
01
0110
01101001
0110100110010110
```

```MODULE ThueMorse;
FROM Strings IMPORT Concat;

PROCEDURE Sequence(steps : CARDINAL);
TYPE String = ARRAY[0..128] OF CHAR;
VAR sb1,sb2,tmp : String;
i : CARDINAL;
BEGIN
sb1 := "0";
sb2 := "1";

WHILE i<steps DO
tmp := sb1;
Concat(sb1, sb2, sb1);
Concat(sb2, tmp, sb2);
INC(i);
END;
WriteString(sb1);
WriteLn;
END Sequence;

BEGIN
Sequence(6);
END ThueMorse.
```

## NewLISP

```(define (Thue-Morse loops)
(setf TM '(0))
(println TM)
(for (i 1 (-- loops))
(setf tmp TM)
(replace '0 tmp '_)
(replace '1 tmp '0)
(replace '_ tmp '1)
(setf TM (append TM tmp))
(println TM)
)
)

(Thue-Morse 5)
(exit)

```

{{out}}

```
(0)
(0 1)
(0 1 1 0)
(0 1 1 0 1 0 0 1)
(0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0)

```

## OASYS Assembler

; Thue-Morse sequence

['A] ; Ensure the vocabulary is not empty [&] ; Declare the initialization procedure %#1> ; Initialize length counter %@> ; Create first object ,#1> ; Initialize loop counter : ; Begin loop %@<.#<PI ; Print current cell *.#%@<.# ; Create new cell %@%@ ; Advance to next cell ,#,# ; Decrement loop counter ,#</ ; Check if loop counter is now zero %#%#<2MUL> ; Double length counter ,#%#<> ; Reset loop counter %@FO> ; Reset object pointer CR ; Line break | ; Repeat loop

```
The standard DOS-based interpreter will display an error message about word too long after 7 lines are output; this is because the 8th line does not fit in 80 columns.

## Objeck

{{trans|Java}}

```objeck
class ThueMorse {
function : Main(args : String[]) ~ Nil {
Sequence(6);
}

function : Sequence(steps : Int) ~ Nil {
sb1 := "0";
sb2 := "1";
for(i := 0; i < steps; i++;) {
tmp := String->New(sb1);
sb1 += sb2;
sb2 += tmp;
};
sb1->PrintLine();
}
}

```

Output:

```
0110100110010110100101100110100110010110011010010110100110010110

```

## OCaml

### By counting ones in binary representation of an iterator

{{trans|C}}

```(* description: Counts the number of bits set to 1
input: the number to have its bit counted
output: the number of bits set to 1 *)
let count_bits v =
let rec aux c v =
if v <= 0 then c
else aux (c + (v land 1)) (v lsr 1)
in
aux 0 v

let () =
for i = 0 to pred 256 do
print_char (
match (count_bits i) mod 2 with
| 0 -> '0'
| 1 -> '1'
| _ -> assert false)
done;
print_newline ()
```

### Using string operations

{{trans|Objeck}}

```let sequence steps =
let sb1 = Buffer.create 100 in
let sb2 = Buffer.create 100 in
for i = 0 to pred steps do
let tmp = Buffer.contents sb1 in
done;
(Buffer.contents sb1)

let () =
print_endline (sequence 6);
```

## Pascal

{{works with|Free Pascal}} Like the C++ Version [[http://rosettacode.org/wiki/Thue-Morse#C.2B.2B]] the lenght of the sequence is given in advance.

```Program ThueMorse;

function fThueMorse(maxLen: NativeInt):AnsiString;
//double by appending the flipped original 0 -> 1;1 -> 0
//Flipping between two values:x oszillating A,B,A,B -> x_next = A+B-x
//Beware A+B < High(Char), the compiler will complain ...
const
cVal0 = '^';cVal1 = 'v';//  cVal0 = '0';cVal1 = '1';

var
pOrg,
pRpl : pChar;
i,k,ml : NativeUInt;//MaxLen: NativeInt
Begin
iF maxlen < 1 then
Begin
result := '';
EXIT;
end;
//setlength only one time
setlength(result,Maxlen);

pOrg := @result[1];
pOrg[0] := cVal0;
IF maxlen = 1 then
EXIT;

pRpl := pOrg;
inc(pRpl);
k := 1;
ml:= Maxlen;
repeat
i := 0;
repeat
pRpl[0] := chr(Ord(cVal0)+Ord(cVal1)-Ord(pOrg[i]));
inc(pRpl);
inc(i);
until i>=k;
inc(k,k);
until k+k> ml;
// the rest
i := 0;
k := ml-k;
IF k > 0 then
repeat
pRpl[0] := chr(Ord(cVal0)+Ord(cVal1)-Ord(pOrg[i]));
inc(pRpl);
inc(i)
until i>=k;
end;

var
i : integer;
Begin
For i := 0 to 8 do
writeln(i:3,'  ',fThueMorse(i));
fThueMorse(1 shl 30);
end.
```

{{Output}}

```Compile with /usr/lib/fpc/3.0.1/ppc386 "ThueMorse.pas" -al -XX -Xs -O4 -MDelphi
without -O4 -> 2 secs
0
1  ^
2  ^v
3  ^vv
4  ^vv^
5  ^vv^v
6  ^vv^v^
7  ^vv^v^^
8  ^vv^v^^v
not written: 1 shl 30 == 1GB
real  0m0.806s user  0m0.563s sys 0m0.242s
```

## Perl

{{works with|Perl|5.x}}

```sub complement
{
my \$s = shift;

\$s =~ tr/01/10/;

return \$s;
}

my \$str = '0';

for (0..6) {
say \$str;
\$str .= complement(\$str);
}

```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Perl 6

{{Works with|rakudo|2018.03}} First 8 of an infinite sequence

```.say for (0, { '0' ~ @_.join.trans( "01" => "10", :g) } ... *)[^8];
```

{{out}}

```0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001
^C
```

## Phix

```string tm = "0"
for i=1 to 8 do
?tm
tm &= sq_sub('0'+'1',tm)
end for
```

{{Out}}

```
"0"
"01"
"0110"
"01101001"
"0110100110010110"
"01101001100101101001011001101001"
"0110100110010110100101100110100110010110011010010110100110010110"
"01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001"

```

## PicoLisp

```(let R 0
(prinl R)
(for (X 1 (>= 32 X))
(setq R
(bin
(pack
(bin R)
(bin (x| (dec (** 2 X)) R)) ) ) )
(prinl (pack 0 (bin R)))
(inc 'X X) ) )
```

## PowerShell

```function New-ThueMorse ( \$Digits )
{
\$ThueMorse = "0"

#  Decrement digits remaining
\$Digits--

#  While we still have digits to calculate...
While ( \$Digits -gt 0 )
{
#  Number of digits we'll get this loop (what we still need up to the maximum available), corrected to 0 base
\$LastDigit = [math]::Min( \$ThueMorse.Length, \$Digits ) - 1

#  Loop through each digit
ForEach ( \$i in 0..\$LastDigit )
{
#  Append the twos complement
\$ThueMorse += ( 1 - \$ThueMorse.Substring( \$i, 1 ) )
}

#  Calculate the number of digits still remaining
\$Digits = \$Digits - \$LastDigit - 1
}

return \$ThueMorse
}

New-ThueMorse 5
New-ThueMorse 16
New-ThueMorse 73
```

{{out}}

```01101
0110100110010110
0110100110010110100101100110100110010110011010010110100110010110100101100
```

## PureBasic

{{trans|C}}

```EnableExplicit

Procedure.i count_bits(v.i)
Define c.i
While v
c+v&1
v>>1
Wend
ProcedureReturn c
EndProcedure

If OpenConsole()
Define n.i
For n=0 To 255
Print(Str(count_bits(n)%2))
Next
PrintN(~"\n...fin") : Input()
EndIf
```

{{out}}

```0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110
...fin
```

## Python

### Python: By substitution

```
m='0'
print(m)
for i in range(0,6):
m0=m
m=m.replace('0','a')
m=m.replace('1','0')
m=m.replace('a','1')
m=m0+m
print(m)

```

{{out}}

```0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
```

### Python: By counting set ones in binary representation

```
>>> def thue_morse_digits(digits):
...     return  [bin(n).count('1') % 2 for n in range(digits)]
...
>>> thue_morse_digits(20)
[0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]

>>>

```

===Python: By [http://mathworld.wolfram.com/SubstitutionSystem.html substitution system]===

```
>>> def thue_morse_subs(chars):
...     ans = '0'
...     while len(ans) < chars:
...         ans = ans.replace('0', '0_').replace('1', '10').replace('_', '1')
...     return ans[:chars]
...
>>> thue_morse_subs(20)
'01101001100101101001'

>>>

```

## R

```
thue_morse <- function(steps) {
sb1 <- "0"
sb2 <- "1"
for (idx in 1:steps) {
tmp <- sb1
sb1 <- paste0(sb1, sb2)
sb2 <- paste0(sb2, tmp)
}
sb1
}
cat(thue_morse(6), "\n")

```

{{out}}

```
0110100110010110100101100110100110010110011010010110100110010110

```

## Racket

```#lang racket
(define 1<->0 (match-lambda [#\0 #\1] [#\1 #\0]))
(define (thue-morse-step (s "0"))
(string-append s (list->string (map 1<->0 (string->list s)))))

(define (thue-morse n)
(let inr ((n (max (sub1 n) 0)) (rv (list "0")))
(if (zero? n) (reverse rv) (inr (sub1 n) (cons (thue-morse-step (car rv)) rv)))))

(for-each displayln (thue-morse 7))
```

{{out}}

```0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
```

## REXX

### using functions

Programming note: ''pop count'' (or ''weight'') is the number of 1's bits in the binary representation of a number.

```/*REXX pgm generates & displays the Thue─Morse sequence up to the Nth term (inclusive). */
parse arg N .                                    /*obtain the optional argument from CL.*/
if N=='' | N==","  then N=80                     /*Not specified?  Then use the default.*/
\$=                                               /*the Thue─Morse sequence  (so far).   */
do j=0  to N                            /*generate sequence up to the Nth item.*/
\$=\$ || \$weight(j) // 2                  /*append the item to the Thue─Morse seq*/
end   /*j*/
say \$
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
\$pop:    return  length( space( translate( arg(1), , 0), 0) )     /*count 1's in number.*/
\$weight: return  \$pop( x2b( d2x( arg(1) ) ) )                     /*dec──►bin, pop count*/
```

'''output''' when using the default input:

```
01101001100101101001011001101001100101100110100101101001100101101001011001101001

```

===using in-line code===

```/*REXX pgm generates & displays the Thue─Morse sequence up to the Nth term (inclusive). */
parse arg N .                                    /*obtain the optional argument from CL.*/
if N=='' | N==","  then N=80                     /*Not specified?  Then use the default.*/
\$=                                               /*the Thue─Morse sequence  (so far).   */
do j=0  to N                            /*generate sequence up to the Nth item.*/
\$=\$ || length( space( translate( x2b( d2x(j) ), , 0), 0) ) // 2  /*append to \$.*/
end   /*j*/
say \$                                            /*stick a fork in it,  we're all done. */
```

'''output''' is identical to the 1st REXX version.

===using 2's complement=== Programming note: this method displays the sequence, but it doubles in (binary) length each iteration.

Because of this, the displaying of the output lacks the granularity of the first two REXX versions.

```/*REXX pgm generates & displays the Thue─Morse sequence up to the Nth term (inclusive). */
parse arg N .                                    /*obtain the optional argument from CL.*/
if N=='' | N==","  then N=6                      /*Not specified?  Then use the default.*/
\$=0                                              /*the Thue─Morse sequence  (so far).   */
do j=1  for N                           /*generate sequence up to the Nth item.*/
\$=\$ || translate(\$, 10, 01)             /*append \$'s  complement to  \$  string.*/
end   /*j*/
say \$                                            /*stick a fork in it,  we're all done. */
```

'''output''' when using the default input:

```
0110100110010110100101100110100110010110011010010110100110010110

```

## Ring

```
tm = "0"
see tm
for n = 1 to 6
tm = thue_morse(tm)
see tm
next

func thue_morse(previous)
tm = ""
for i = 1 to len(previous)
if (substr(previous, i, 1) = "1") tm = tm + "0" else tm  = tm + "1" ok
next
see nl
return (previous + tm)

```

Output:

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Ruby

```puts s = "0"
6.times{puts s << s.tr("01","10")}
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## Rust

```const ITERATIONS: usize = 8;

fn neg(sequence: &String) -> String {
sequence.chars()
.map(|ch| {
(1 - ch.to_digit(2).unwrap()).to_string()
})
.collect::<String>()
}

fn main() {
let mut sequence: String = String::from("0");
for i in 0..ITERATIONS {
println!("{}: {}", i + 1, sequence);
sequence = format!("{}{}", sequence, neg(&sequence));
}
}
```

{{out}}

```
1: 0
2: 01
3: 0110
4: 01101001
5: 0110100110010110
6: 01101001100101101001011001101001
7: 0110100110010110100101100110100110010110011010010110100110010110
8: 01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001

```

## Scala

```def thueMorse(n: Int): String = {
val (sb0, sb1) = (new StringBuilder("0"), new StringBuilder("1"))
(0 until n).foreach { _ =>
val tmp = sb0.toString()
sb0.append(sb1)
sb1.append(tmp)
}
sb0.toString()
}

(0 to 6).foreach(i => println(s"\$i : \${thueMorse(i)}"))
```

{{Out}} See it running in your browser by [https://scastie.scala-lang.org/rsF3Y5ABQoK0zZMMA3m6Ow Scastie (JVM)].

## Sidef

```func recmap(repeat, seed, transform, callback) {
func (repeat, seed) {
callback(seed)
repeat > 0 && __FUNC__(repeat-1, transform(seed))
}(repeat, seed)
}

recmap(6, "0", {|s| s + s.tr('01', '10') }, { .say })
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```

## SQL

This example is using SQLite.

```with recursive a(a) as (select '0' union all select replace(replace(hex(a),'30','01'),'31','10') from a) select * from a;
```

You can add a LIMIT clause to the end to limit how many lines of output you want.

## Tcl

Since string map correctly handles overlapping replacements, the simple map 0 -> 01; 1 -> 10 can be applied with no special handling:

```proc tm_expand {s} {string map {0 01 1 10} \$s}
# this could also be written as:
# interp alias {} tm_expand {} string map {0 01 1 10}

proc tm {k} {
set s 0
while {[incr k -1] >= 0} {
set s [tm_expand \$s]
}
return \$s
}
```

Testing:

```for {set i 0} {\$i <= 6} {incr i} {
puts [tm \$i]
}
```

{{out}}

```0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
```

For giggles, also note that the above SQL solution can be "natively" applied in Tcl8.5+, which bundles Sqlite as a core extension:

```
package require sqlite3 ;# available with Tcl8.5+ core
sqlite3 db ""           ;# create in-memory database
set LIMIT 6
db eval {with recursive a(a) as (select '0' union all select replace(replace(hex(a),'30','01'),'31','10') from a) select a from a limit \$LIMIT} {
puts \$a
}
```

## uBasic/4tH

For x = 0 to 6 ' sequence loop Print Using "_#";x;": "; ' print sequence For y = 0 To (2^x)-1 ' element loop Print AND(FUNC(_Parity(y)),1); ' print element Next ' next element Print ' terminate elements line Next ' next sequence

End

_Parity Param (1) ' parity function Local (1) ' number of bits set b@ = 0 ' no bits set yet Do While a@ # 0  ' until all bits are counted If AND (a@, 1) Then b@ = b@ + 1 ' bit set? increment count a@ = SHL(a@, -1) ' shift the number Loop Return (b@) ' return number of bits set

```
{{Out}}

```txt
0: 0
1: 01
2: 0110
3: 01101001
4: 0110100110010110
5: 01101001100101101001011001101001
6: 0110100110010110100101100110100110010110011010010110100110010110

0 OK, 0:123
```

## VBA

```Option Explicit

Sub Main()
Dim i&, t\$
For i = 1 To 8
t = Thue_Morse(t)
Debug.Print i & ":=> " & t
Next
End Sub

Private Function Thue_Morse(s As String) As String
Dim k\$
If s = "" Then
k = "0"
Else
k = s
k = Replace(k, "1", "2")
k = Replace(k, "0", "1")
k = Replace(k, "2", "0")
End If
Thue_Morse = s & k
End Function
```

{{Out}}

```1:=> 0
2:=> 01
3:=> 0110
4:=> 01101001
5:=> 0110100110010110
6:=> 01101001100101101001011001101001
7:=> 0110100110010110100101100110100110010110011010010110100110010110
8:=> 01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001
```

## XLISP

```(defun thue-morse (n)
(defun flip-bits (s)
(defun flip (l)
(if (not (null l))
(cons
(if (equal (car l) #\1)
#\0
#\1)
(flip (cdr l)))))
(list->string (flip (string->list s))))
(if (= n 0)
"0"
(string-append (thue-morse (- n 1)) (flip-bits (thue-morse (- n 1))))))

; define RANGE, for testing purposes

(defun range (x y)
(if (< x y)
(cons x (range (+ x 1) y))))

; test THUE-MORSE by printing the strings it returns for n = 0 to n = 6

(mapcar (lambda (n) (print (thue-morse n))) (range 0 7))
```

{{out}}

```"0"
"01"
"0110"
"01101001"
"0110100110010110"
"01101001100101101001011001101001"
"0110100110010110100101100110100110010110011010010110100110010110"
```

## Yabasic

{{trans|Phix}}

```tm\$ = "0"
for i=1 to 8
? tm\$
tm\$ = tm\$ + inverte\$(tm\$)
next

sub inverte\$(tm\$)
local i

for i = 1 to len(tm\$)
mid\$(tm\$, i, 1) = str\$(not val(mid\$(tm\$, i, 1)))
next
return tm\$
end sub
```

## zkl

```fcn nextTM(str){ str.pump(str,'-.fp("10")) } // == fcn(c){ "10" - c }) }
```

"12233334444" - "23"-->"14444"

```str:="0"; do(7){ str=nextTM(str.println()) }
```

println() returns the result it prints (as a string). {{trans|Java}}

```fcn nextTM2{
var sb1=Data(Void,"0"), sb2=Data(Void,"1");
r:=sb1.text; sb1.append(sb2); sb2.append(r);
r
}
```
```do(7){ nextTM2().println() }
```

{{out}}

```
0
01
0110
01101001
0110100110010110
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110

```