Collatz's ice cream cone factory

Question

The Collatz sequence

Given a positive integer \$a_1\$, the Collatz sequence with starting value \$a_1\$ is defined as \begin{equation} a_{n+1} = \begin{cases} a_n/2 & \mathrm{if}\ a_n\ \mathrm{is}\ \mathrm{even} \\ 3a_n+1 & \mathrm{if}\ a_n\ \mathrm{is}\ \mathrm{odd}. \end{cases} \end{equation} It is conjectured that, for any starting value, this sequence always reaches the number \$1\$. This challenge assumes that the conjecture is true.

The challenge

Given an integer \$a_1 > 2\$, compute the Collatz sequence until \$1\$ is reached for the first time. Let \$N\$ be the number of sequence terms (including \$a_1\$ and \$a_N = 1\$). From the sequence of numbers \begin{equation} a_1, a_2, a_3, \ldots, a_N \end{equation} form a sequence of points in the plane by taking all pairs of consecutive terms \begin{equation} (a_1, a_2), (a_2, a_3), \ldots, (a_{N-1}, a_N) \end{equation} and plot these points on a 2D graph, joining consecutive points by a line segment.

Example

For input \$12\$ the Collatz sequence is (\$10\$ terms); \begin{equation} 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. \end{equation} The sequence of points is (\$9\$ points): \begin{equation} (12, 6), (6, 3), (3, 10), (10, 5), (5, 16), (16, 8), (8, 4), (4, 2), (2, 1). \end{equation} The plot contains \$8\$ line segments, as shown in the following graph. Note that some of the segments partially overlap. For clarity, the plot includes markers at the \$9\$ points.

Additional rules

• Graphical output is required, with output being flexible as usual.
• Only the straight lines are required in the graph. Line width is flexible, as long as the plot can be seen reasonably well. Line color is also flexible, and may be different for each segment, as long as lines are distinguishable from the background.
• Other elements in the graph are not required, but are allowed (point markers, grid lines, axis labels, ...).
• Horizontal and vertical axis scales need not be the same. Axis limits are arbitrary, as long as the graph can be seen fully and clearly. The axes may be swapped, and each axis may be reversed.
• The code should work for any input given unlimited resources. It is acceptable if in practice it fails for large inputs due to time, memory or data-type limitations.
• If the input happens to be a counterexample for the Collatz conjecture the code can do anything, such as get stuck in an infinite loop or order a pizza.
• Programs or functions are accepted. Standard loopholes are forbidden.
• Shortest code in bytes wins.

Test cases

Input	Output
3
4
27
649
650
46720
345435
63728127

Answer 1

Python 3.8 with turtle, 156 127 bytes

Thanks to Noodle9 for catching a mistake!

from turtle import*
def f(n,x=0):
 while~-n:goto(w:=n,n:=[n//2,3*n+1][n%2]);x<1!=clear();setworldcoordinates(0,0,x:=max(x,n),x)

Animation for \$a_1=27\$:

Answer 2

J, 52 bytes

load 'plot'
f=:[:plot[:(}:;}.)(2&|{-:,1+*&3)^:(>&1)^:a:

Try it online!

Wasn't sure if loading the graphics lib counted towards byte count, so I included it.

Here's an image of calling f 27 in the J console:

Answer 3

Jelly, 35 bytes

r0×€:⁸
×3‘ƊHḂ?Ƭ;Ɲ_/AÞṪçƊ+ṪƲƝẎŒṬx€€3

Try it online!

A pair of links that takes an integer argument and returns an RGB matrix on the (0 to 1) scale. Approach is the same as PBM output below but loses some bytes from the simpler output format.

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Previous PBM answer Jelly, 49 44 bytes

r0×€:⁸
×3‘ƊHḂ?Ƭ;Ɲ_/AÞṪçƊ+ṪƲƝẎŒṬµZL;L;FKṭ“P1 

Try it online!

A full program that takes an integer argument and prints the contents of a PBM file.

Thanks to @cairdcoinheringaahing for some nice golfs totally 5 bytes!

Example for 22:

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Original SVG-based answer: Jelly, 83 bytes

×3‘ƊHḂ?Ị¬$пµj”,$ƝKṭṀ,`$“¡×ȯFṗẓ"az⁺Ṭ*,ġẎlḣḂ⁷Ọ]Ẏɦ?÷hṖF.IØṣƘŻÇÄ<,Ḥ:ẆṡṂȮXȷḷ[eʂmJ]»Ỵ¤;"

Try it online!

A full program taking an integer argument and printing an SVG.

For example, with 45:

<svg width="136" height="136"><path stroke="red" fill="none" d="M45,136 136,68 68,34 34,17 17,52 52,26 26,13 13,40 40,20 20,10 10,5 5,16 16,8 8,4 4,2 2,1"/></svg>

Answer 4

R >= 4.1, 81 74 bytes

\(x,y=x){while(x>1)y=c(y,x<-c(x/2,3*x+1)[x%%2+1]);plot(y,c(y[-1],NA),"l")}

Try it at RDRR.io!

Note this uses RDRR because TIO doesn’t support graphical output. It also uses function in place of \ since RDRR doesn’t support R 4.1.0 yet.

Thanks to @DominicVanEssen for saving 7 bytes!

Answer 5

Wolfram Language (Mathematica), 70 bytes

Graphics@Line@Last@Reap[#//.a_/;a>1:>Last@Sow@{a,If[2∣a,a/2,3a+1]}]&

-17 bytes from @att

63728127

Answer 6

Julia using GR, 121 99 77 bytes

Even better version by @MarcMush:

using GR
!x=while(X=x[end])>1 plot([x;],(x=[x;X%2>0 ? 3X+1 : X/2])[2:end])end

Improved version thanks to the tips found here:

using GR
c(a)=(i=1;while a[i]>1 a=[a;%(a[i],2)>0 ? 3a[i]+1 : a[i]/2];i+=1end;plot(a[1:i-1],a[2:i]))

What has been done:

• single-line notation for functions -10 bytes
• replace push! by array concatenation -3 bytes
• use input a as array - 6 bytes
• replace end by variable i that stores the length -3 bytes

Original version:

using GR
function c(x) a=[x]
while a[end]>1 push!(a,%(a[end],2)>0 ? 3a[end]+1 : a[end]/2)end
plot(a[1:end-1],a[2:end])end

Calling c(27) gives:

Answer 7

SageMath, ^{81 \$\cdots\$ 74} 71 bytes

Saved 3 bytes thanks to dingledooper!!!

f=lambda n,*r:n-1and f(c:=[n/2,3*n+1][n%2],*r,(n,c))or list_plot(r,1<2)

Try it online!

f(63728127)

Answer 8

Red, ²³⁰ 212 bytes

func[n][a: to[]n while[n > 1][append a n: either odd? n[3 * n + 1][n / 2]]to-pair m: last sort copy a view[base 500x500 draw append[line]collect[while[a/2][keep as-pair a/1 / m * 500(first a: next a)/ m * 500]]]]

Try it online!

I don't know if red has a scalable plotting mechanism, but this was what I managed to get using the draw dialect. All outputs are scaled to 500x500 and there may be some inaccuracies for larger inputs due to downscaling and pairs being integers.

In the red interpreter, you will have to redefine the function before each run because the words get messed up.

-4 after using default axes.

-18 bytes from Galen Ivanov.

Output(n=12) (old)

Answer 9

Factor + ui.gadgets.charts ui.gadgets.charts.lines math.unicode, ^{208 204} 199 bytes

[ [ [ 3 dupn , odd? [ 3 * 1 + ] [ 2/ ] if dup 1 ≠ ] loop , ] f make chart new over supremum 1 + '[ 0 _ ] dup 2array >>axes line new COLOR: red >>color rot 2 clump >>data add-gadget "" open-window ]

It's quotation (anonymous function) that accepts an integer from the data stack and opens a window with the chart in it. This only works in recent-ish builds of Factor, as the chart gadget is fairly new; I used build 2074. Here's what it looks like for an input of 27:

Unfortunately, the chart gadget doesn't come with any constructors. It requires us to manually calculate axes, and build its subcomponents which themselves don't come with any constructors. This leads to a bit of verbosity.

Answer 10

HTML + JS, 166 bytes

JS: 156 bytes

HTML: 14 bytes

This is a pretty basic implementation that renders to the DOM using an HTML canvas. A good chunk of the code is spent scaling the output to fit within the canvas. Anyone got any better ideas to handle this?

The input is specified inline in the code, set the number inside x=[...].

x=[9];c=C.getContext`2d`;c.beginPath();while((z=x[0])-1)x.unshift(z%2?3*z+1:z/2);r=Math.max(...x)/99;x.map((a,i)=>c.lineTo(a/r,99-x[i-1]/r));c.stroke()

<canvas id=C>

Answer 11

Python 3 + matplotlib, 127 bytes

def f(n,r=[]):
 k=n
 while ~-n:n=[n//2,3*n+1][n%2];r+=[n]
 p.plot(*zip(*[[k]+r,r]),'-o');p.show()
import matplotlib.pyplot as p

-5 bytes thanks to @ovs!!!

Answer 12

MATLAB 1999, 95 84 bytes

-1 from Luis Mendo

n=input('');i=n;while i>1;i=(i+mod(i,2)*(5*i+2))/2;n=[n;i];end;plot([0/0;n],[n;0/0])

Even A(2:) and A(2:-1)` was unavailable at that time...

Answer 13

Python + Pygame, 228 bytes

from pygame import*
d=display
n=int(input())
k=[]
while n>1:k+=[[n,n:=[n//2,3*n+1][n%2]]]
M=max(k)[0]
S=500
g=lambda s:[S*s[0]/M,S*s[1]/M]
s=d.set_mode([S,S])
for i,j in enumerate(k):draw.line(s,[99]*3,g(k[i-1]),g(j))
d.update()

No TIO link because Pygame is not supported there.

Reversed y-axis.

I could save one byte by setting S to 99 or something, but I chose not to for easier viewing. I could also change [99]*3 to [9]*3 but I chose not to for easier viewing.

Here is an example for input 63728127: