Questions tagged [fractal]

Fractals are shapes that are self-similar and are usually quite detailed. Well-known fractal sets include the Mandelbrot set, Julia sets, and Phoenix sets. Tree-like fractal drawings are also common.

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Mandelbrot image in every language

I always used a Mandelbrot image as the 'graphical' version of Hello World in any graphical application I got my hands on. Now it's your guys' turn. Language must be capable of graphical output or ...
Mark Jeronimus's user avatar
80 votes
30 answers
12k views

Create an "H" from smaller "H"s

Challenge Create a function or program that, when given an integer size, does the following: If size is equal to 1, output ...
Bazinga_9000's user avatar
53 votes
31 answers
11k views

Generate a mandelbrot fractal [closed]

Your task is to draw the mandelbrot set in ascii. It should look something like The complex number c lies in the mandelbrot set, when the sequence ...
Hannesh's user avatar
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50 votes
3 answers
3k views

Help, I'm trapped in a Sierpinski triangle!

Drawing the Sierpinski triangle has been done to death. There's other interesting things we can do with it though. If we squint hard enough at the triangle, we can view upside-down triangles as nodes ...
Martin Ender's user avatar
49 votes
26 answers
11k views

Draw the Devil's Staircase

The Devil's Staircase is a fractal-like function related to the Cantor set. Your task is to replicate this funky function — in ASCII art! Input A single integer ...
Sp3000's user avatar
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49 votes
3 answers
5k views

Computer Generated Textured Wall Paint

The paint on the walls in my room has a random, almost fractal-like, 3-dimensional texture: In this challenge you will write a program that generates random images that look like they could be part ...
Calvin's Hobbies's user avatar
48 votes
16 answers
5k views

Sierpinskified Code

Write a rectangular block of text that when arranged into a Sierpinski carpet, using same-sized blocks of spaces for the empty portions, creates a program that outputs the iteration number of the ...
Calvin's Hobbies's user avatar
47 votes
41 answers
19k views

Draw A Sierpinski Triangle

The Sierpinsky Triangle is a fractal created by taking a triangle, decreasing the height and width by 1/2, creating 3 copies of the resulting triangle, and place them such each triangle touches the ...
Kibbee's user avatar
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45 votes
4 answers
2k views

Computer Generated Cracked Soil

Write a program that takes in an integer from 0 to 65535 (216-1) and generates a unique 500×500 pixel image that looks as similar as possible to these 6 real life images of cracked soil: These ...
Calvin's Hobbies's user avatar
36 votes
10 answers
3k views

Generate fractals from bit patterns in ASCII

Overview Write a program that prints out simple fractal patterns given a bit pattern encoding the fractal, plus the per-generation scale factor of the fractal and number of generations. Explanation ...
samgak's user avatar
  • 1,677
34 votes
6 answers
1k views

Generate a Padovan Spiral

Introduction Similar to the Fibonacci Sequence, the Padovan Sequence (OEIS A000931) is a sequence of numbers that is produced by adding previous terms in the sequence. The initial values are defined ...
Andrew Li's user avatar
  • 1,071
34 votes
1 answer
1k views

Gasket Weaving - draw a Sierpiński knot

Given an integer N >= 2, produce an image showing a Sierpiński knot of degree N. For example, here are knots of degree 2, 3, 4 and 5: Click on the images to view full size (the higher the degree the ...
trichoplax is on Codidact now's user avatar
33 votes
24 answers
3k views

The IHIH Pyramid

I find it fascinating how the letters "H" and "I" are very similar. "H" is a horizontal stroke surrounded by two vertical strokes; "I" is a vertical stroke surrounded by two horizontal strokes (...
DJMcMayhem's user avatar
32 votes
9 answers
4k views

ASCII Art of the Day #2 - Flow Snakes

A Flow Snake, also known as a Gosper curve, is a fractal curve, growing exponentially in size with each order/iteration of a simple process. Below are the details about the construction and a few ...
Optimizer's user avatar
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31 votes
6 answers
3k views

Draw the Hilbert curve using slashes

The Hilbert curve is a space filling fractal that can be represented as a Lindenmayer system with successive generations that look like this: Thanks to http://www.texample.net/tikz/examples/hilbert-...
Calvin's Hobbies's user avatar
30 votes
14 answers
3k views

Generate TeX to typeset Sierpinski Triangle Fractal

Challenge Write code that outputs TeX (LaTeX) math-equation code (given below) that will typeset Sierpinski Triangle Fractal of 5 levels. Shortest code wins. Details TeX (and friends like LaTeX, ...
Vitaliy Kaurov's user avatar
29 votes
10 answers
5k views

Play the Chaos Game

The Chaos Game is a simple method to generate fractals. Given a starting point, a length ratio r and a set of 2D points, repeatedly do the following: From your set of points, pick one at random (...
Martin Ender's user avatar
29 votes
4 answers
5k views

Draw an Apollonian Gasket

Given three mutually tangent circles, we can always find two more circles which are tangent to all three of those. These two are called Apollonian circles. Note that one of the Apollonian circles ...
Martin Ender's user avatar
29 votes
2 answers
920 views

Hilbertify an image

I like the Hilbert Curve. Your task for this challenge is to take an image (strictly a square image where all the sides are a power of two pixels wide) and unravel it line by line in a zig-zagging ...
Wheat Wizard's user avatar
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28 votes
5 answers
1k views

The Image of the Dragon

I saw a cool gif of the twin dragon curve made from a square, and wondered what would happen if we started from another base image. So I wrote a program to do this.                                    ...
Wheat Wizard's user avatar
  • 97.6k
27 votes
4 answers
1k views

Map string to Hilbert curve

Let's map some strings to 2d space, fractal style. Your task is to compute a Hilbert curve and lay a string along it. Task The task is to take the single-line input string, and lay it out along a ...
wizzwizz4's user avatar
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26 votes
30 answers
5k views

Sierpinski Carpets

Who doesn't love a good fractal? The Sierpinski Carpet is a classic example of a fractal. To complete this task, you will be required to generate a carpet of type \$n\$ and print the resulting image ...
Paul Clavier's user avatar
26 votes
7 answers
815 views

ASCII Cayley Graph

While doing some research for a different challenge I'm formulating, I came across a Cayley graph, specifically this one. Since I'm one of the top ascii-art challenge writers, of course I had to make ...
AdmBorkBork's user avatar
  • 43.3k
26 votes
5 answers
2k views

ASCII Dragon's Curve

Introduction The Dragon's Curve is a fractal curve that notably appears on section title pages of the Jurassic Park novel. It can very simply be described as a process of folding a paper strip, as ...
Fatalize's user avatar
  • 38.5k
26 votes
11 answers
707 views

Binary tree fractal

Today's challenge is to draw a binary tree as beautiful ascii-art like this example: ...
DJMcMayhem's user avatar
25 votes
2 answers
1k views

ASCII Hilbert Curve

Given an integer n output the nth iteration of the Hilbert Curve in ASCII using the characters ...
Bobas_Pett's user avatar
  • 1,025
24 votes
20 answers
4k views

Print a Cantor Set

The Challenge Build a N-Leveled Cantor Set. The Cantor ternary set is created by repeatedly deleting the open middle thirds of a set of line segments. The program receives one parameter ...
Averroes's user avatar
  • 4,087
24 votes
3 answers
7k views

Generate Newton fractals

You all know the Newton method to approximate the roots of a function, don't you? My goal in this task is to introduce you into an interesting aspect of this algorithm. Newton's algorithm converges ...
FUZxxl's user avatar
  • 10.1k
24 votes
1 answer
395 views

It's factors all the way down!

This challenge is inspired by this fantastic animated diagram (thanks to flawr for posting it in chat). Given an input n, draw all of its prime factors as nested ...
Sherlock9's user avatar
  • 12.2k
23 votes
14 answers
3k views

The Cantor Function

The Cantor function is continuous everywhere and constant almost everywhere, but has an average slope of 1: The function can be found recursively: \$f_0(x)=x\$ \$f_{n+1}(x)=\left\{\begin{matrix}\frac{...
golf69's user avatar
  • 2,059
23 votes
12 answers
2k views

Quicksand (piles)

In this fastest-code challenge, you take a positive integer as input, which represents the height of a sand pile, located at (0,0) on an infinite square grid. For example, if our input is ...
AnttiP's user avatar
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23 votes
2 answers
2k views

Eye test - How many squares are in this picture?

The picture: Sick of the same old grid where the answer is simply a square pyramidal number? Accept the challenge and write a program that given a positive integer \$n\$ counts how many squares are ...
Domenico's user avatar
  • 2,253
22 votes
5 answers
6k views

"Sorry, young man, but it's Turtles all the way down!"

Execute a Lindenmayer System A Lindenmayer System (or L-system) is related to Thue and Post systems, and is used in botanical modeling and fractal generation. An L-system is described by string-...
luser droog's user avatar
  • 4,907
22 votes
24 answers
4k views

Fractal Cathedral

Given a positive integer n >= 1, output the first n rows of the following structure: ...
hyper-neutrino's user avatar
  • 41.4k
22 votes
9 answers
1k views

Unicode T-square

Challenge Create a function or program that, when given an integer size, behaves the following way: If size is equal to 1, ...
zdimension's user avatar
22 votes
6 answers
3k views

Koch Snowflake - codegolf

The Koch snowflake (also known as the Koch star and Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in ...
gnibbler's user avatar
  • 15.1k
21 votes
13 answers
7k views

Draw a Dragon Curve

You task for today: draw a dragon curve! In case you don't know what a Dragon Curve is, here is an introductory ViHart video (Really cool, please watch!) Your task: draw a dragon curve, iterated at ...
Alecto Irene Perez's user avatar
21 votes
7 answers
1k views

The strange attraction of the logistic map

The purpose of the challenge is to approximately plot the attractor of the logistic map as a function of its parameter r (also called bifurcation diagram), or a subregion of it. The appearance of the ...
Luis Mendo's user avatar
  • 104k
20 votes
13 answers
1k views

Sierpinski Layers

Starting with /\ you can create a Sierpinski triangle like pattern by adding a line beneath such that... Any loose branch / or <...
Calvin's Hobbies's user avatar
20 votes
9 answers
2k views

Is it within the Cantor set?

The Challenge For this challenge, you are supposed to determine if a given number is in the Cantor set. So first, let's define the Cantor set. First, start with the numbers between 0 and 1. Any ...
TheNumberOne's user avatar
  • 11.5k
18 votes
6 answers
1k views

Draw this fractal generated by applying Newton's method to cosh(x) - 1

I came across this picture the other day: (Credit to Josep M Batlle I Ferrer) Your job is to generate this picture. This graph is generated by repeatedly applying newton's method to the graph of: $$f(...
mousetail's user avatar
  • 12.4k
18 votes
1 answer
471 views

Make Some Snow!

Your task: generate a Koch snowflake to the nth depth. You do not need to make a complete Koch snowflake, just one side of the starting triangle. Wikipedia on Koch flakes: https://en.wikipedia.org/...
sporkl's user avatar
  • 6,824
17 votes
22 answers
2k views

Compute this fractal matrix

The unique-disjointness matrix ( UDISJ(n) ) is a matrix on all pairs of subsets of {1...,n} with entries $$ U_{(A,B)}=\begin{cases} 0, ~ if ~ |A\cap B|=1\\ 1, ~ ...
bsoelch's user avatar
  • 5,945
17 votes
11 answers
3k views

Fibonacci word fractal

The Fibonacci word is a sequence of binary strings defined as: \$F_0 = \$ 0 \$F_1 = \$ 01 \$F_n = F_{n-1} F_{n-2}\$ The first ...
alephalpha's user avatar
  • 47.5k
17 votes
12 answers
613 views

Generalized Cantor set segment lengths

Problem Let's define a generalized Cantor set by iteratively deleting some rational length segments from the middle of all intervals that haven't yet been deleted, starting from a single continuous ...
Angs's user avatar
  • 4,957
16 votes
8 answers
8k views

Create a fractal tree

What I would like to see is a fractal tree being drawn where the you can input an integer, and the output will be a fractal tree with the entered amount of branch steps. Rules: The fractal should be ...
joeytje50's user avatar
  • 621
16 votes
9 answers
3k views

Drawing the Peano curve

Introduction In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit ...
Peiffap's user avatar
  • 287
16 votes
6 answers
865 views

Converging Sums of a Fractal Sequence

Background A fractal sequence is an integer sequences where you can remove the first occurrence of every integer and end up with the same sequence as before. A very simple such sequence is called ...
Martin Ender's user avatar
16 votes
4 answers
1k views

Create a triangle whose colors are determined by the bitsums of coordinates

Write a program that, for any \$n\$, generates a triangle made of hexagons as shown, \$2^n\$ to a side. The colors are to be determined as follows. We may give the triangle barycentric coordinates so ...
Akiva Weinberger's user avatar
16 votes
3 answers
877 views

ASCII L-system renderer

Background An L-system (or Lindenmayer system) is a parallel rewriting system that, among other things, can be easily used to model fractals. This question concerns deterministic, context-free L-...
Uri Granta's user avatar
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