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Thue-Morse: Difference between revisions

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Thue-Morse (view source)

Revision as of 17:08, 16 April 2024

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Line 15:
 
<syntaxhighlight lang="11l">F thue_morse_digits(digits)
R (0 .< digits).map(n -> binbits:popcount(n).count(‘1’) % 2)
 
print(thue_morse_digits(20))</syntaxhighlight>
Line 180:
0110100110010110100101100110100110010110011010010110100110010110
</pre>
 
=={{header|APL}}==
<syntaxhighlight lang="apl">⍝ generate the first ⍵ elements of the Thue-Morse sequence
tm←{⍵⍴(⊢,~)⍣(⍵≤(⍴⊢))⊢,0}</syntaxhighlight>
{{out}}
<pre> tm 32
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</pre>
 
=={{header|AppleScript}}==
Line 480 ⟶ 487:
{{out}}
<pre>0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110</pre>
 
=={{header|Binary Lambda Calculus}}==
 
The (infinite) Thue-Morse sequence is output by the 115 bit BLC program
 
<pre>0001000110100001010100011010000000000101101110000101100000010111111101011001111001111110111110000011001011010000010</pre>
 
as documented in https://github.com/tromp/AIT/blob/master/characteristic_sequences/thue-morse.lam
 
Output:
 
<pre>01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100101101001...</pre>
 
=={{header|BQN}}==
Line 875 ⟶ 894:
{{out}}
<pre>0110100110010110100101100110100110010110011010010110100110010110</pre>
 
=={{header|EasyLang}}==
{{trans|BASIC256}}
<syntaxhighlight>
func$ tmorse s$ .
for i to len s$
if substr s$ i 1 = "1"
k$ &= "0"
else
k$ &= "1"
.
.
return s$ & k$
.
tm$ = "0"
print tm$
for j to 7
tm$ = tmorse tm$
print tm$
.
</syntaxhighlight>
 
=={{header|Elena}}==
{{trans|C#}}
ELENA 46.x :
<syntaxhighlight lang="elena">import extensions;
import system'text;
Line 886 ⟶ 926:
var sb1 := TextBuilder.load("0");
var sb2 := TextBuilder.load("1");
for(int i := 0,; i < steps,; i += 1)
{
var tmp := sb1.Value;
Line 1,140 ⟶ 1,180:
| 0110100110010110100101100110100110010110011010010110100110010110
|}
 
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Thue-Morse. Nigel Galloway: April 16th., 2024
let rec fG n g=match n with 0->g |1->g+1 |n ->fG(n/2)(g+n&&&1)
let thueMorse=Seq.initInfinite(fun n->(fG n 0)%2)
thueMorse|>Seq.take 25|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
 
=={{header|Factor}}==
Line 1,271 ⟶ 1,323:
=={{header|Fōrmulæ}}==
 
{{FormulaeEntry|page=https://formulae.org/?script=examples/Thue-Morse}}
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation &mdash;i.e. XML, JSON&mdash; they are intended for storage and transfer purposes more than visualization and edition.
 
=== Solution 1 ===
 
[[File:Fōrmulæ - Thue–Morse sequence 01.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 11.png]]
 
=== Solution 2 ===
 
[[File:Fōrmulæ - Thue–Morse sequence 02.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 11.png]]
 
=== Solution 3 ===
 
[[File:Fōrmulæ - Thue–Morse sequence 03.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 11.png]]
 
=== Solution 4 ===
 
Notice that this solution generates a string.
 
[[File:Fōrmulæ - Thue–Morse sequence 04.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 12.png]]
 
=== Solution 5 ===
 
Notice that this solution generates a string.
 
[[File:Fōrmulæ - Thue–Morse sequence 05.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 12.png]]
 
=== Solution 6 ===
 
Notice that this solution generates a string.
 
[[File:Fōrmulæ - Thue–Morse sequence 06.png]]
 
[[File:Fōrmulæ - Thue–Morse sequence 12.png]]
 
=== Solution 7. L-system ===
 
There are generic functions written in Fōrmulæ to compute an L-system in the page [[L-system#Fōrmulæ | L-system]].
 
The program that creates a Hilbert curve is:
 
[[File:Fōrmulæ - L-system - Thue-Morse 01.png]]
Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
 
[[File:Fōrmulæ - Thue–Morse sequence 12.png]]
In '''[https://formulae.org/?example=Thue-Morse this]''' page you can see the program(s) related to this task and their results.
 
=={{header|Go}}==
Line 1,757 ⟶ 1,857:
0110100110010110...transmitted
</pre>
 
=={{header|MACRO-11}}==
<syntaxhighlight lang="macro11"> .TITLE THUE
.MCALL .TTYOUT,.EXIT
THUE:: MOV #100,R3 ; 64 ITEMS
CLR R2
1$: JSR PC,SEQ ; GET THUE-MORSE SEQUENCE ITEM
ADD #60,R0 ; MAKE ASCII
.TTYOUT ; PRINT
INC R2
SOB R3,1$
.EXIT
 
; LET R0 = R2'TH ITEM IN THUE MORSE SEQUENCE
SEQ: CLR R0
MOV #20,R1
1$: ROR R0
XOR R2,R0
SOB R1,1$
BIC #^C1,R0
RTS PC
.END THUE</syntaxhighlight>
{{out}}
<pre>0110100110010110100101100110100110010110011010010110100110010110</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
Line 1,762 ⟶ 1,886:
{{out}}
<pre>{1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0}</pre>
 
=={{header|MATLAB}}==
===MATLAB: By counting set ones in binary representation===
<syntaxhighlight lang="MATLAB">
tmSequence = thue_morse_digits(20);
disp(tmSequence);
 
function tmSequence = thue_morse_digits(n)
tmSequence = zeros(1, n);
for i = 0:(n-1)
binStr = dec2bin(i);
numOnes = sum(binStr == '1');
tmSequence(i+1) = mod(numOnes, 2);
end
end
</syntaxhighlight>
{{out}}
<pre>
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1
</pre>
 
 
=={{header|Miranda}}==
Line 2,364 ⟶ 2,509:
01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001
^C</pre>
 
=={{header|Refal}}==
<syntaxhighlight lang="refal">$ENTRY Go {
= <Prout <ThueMorse 7>>
};
 
ThueMorse {
0 e.X = e.X;
s.N e.X = <ThueMorse <- s.N 1> <ThueMorseStep e.X>>;
};
 
ThueMorseStep {
= '0';
e.X = e.X <Invert e.X>;
};
 
Invert {
= ;
'0' e.X = '1' <Invert e.X>;
'1' e.X = '0' <Invert e.X>;
};</syntaxhighlight>
{{out}}
<pre>0110100110010110100101100110100110010110011010010110100110010110</pre>
 
=={{header|REXX}}==
Line 2,439 ⟶ 2,607:
01101001100101101001011001101001
0110100110010110100101100110100110010110011010010110100110010110
</pre>
 
=={{header|RPL}}==
{{works with|HP|48G}}
We use here the bitwise negation method: it needs few words and is actually faster than the "fast" generation method, because RPL is better in list handling than in bitwise calculations.
≪ { 0 }
'''WHILE''' DUP2 SIZE > '''REPEAT'''
1 OVER - +
'''END'''
1 ROT SUB
≫ '<span style="color:blue">THUEM</span>' STO
 
20 <span style="color:blue">THUEM</span>
{{out}}
<pre>
1: { 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 }
</pre>
 
Line 2,657 ⟶ 2,841:
=={{header|Wren}}==
{{trans|Kotlin}}
<syntaxhighlight lang="ecmascriptwren">var thueMorse = Fn.new { |n|
var sb0 = "0"
var sb1 = "1"
Nigel Galloway
2,171

edits

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