52 ideas
Checked October 2026

Easy Fractals to Draw

Press for an easy fractal to draw, with the one rule to repeat written out in words.

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Drawn: Sierpiński triangle after one cut: three corners leftSierpiński triangle after one cut: three corners leftSplit a triangle into four equal ones and remove the middle. Repeat that one move in each corner.

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All 52 ideas

Triangles and snowflakes 13

A hexaflake: seven hexagons inside one Put a small hexagon at each corner of a large one and one in the middle. Repeat inside each.
A Koch curve grown from a single straight line Split a line into three, raise a triangle on the middle third and erase its base. Repeat on each line.
A Koch snowflake at stage one: a six-pointed star Start from a triangle with three equal sides and put one outward bump on each side.
A Minkowski sausage: one line broken into eight Replace each line with a broken line of eight parts, each a quarter as long. Repeat on every part.
A pentaflake: six pentagons inside one Put a small pentagon in each corner of a large one and one in the center. Treat each small one the same.
A quadratic Koch curve: square bumps along a line The Koch rule with squares for triangles: raise a square bump on the middle third of every line.
A Sierpiński arrowhead curve, one unbroken line A single path that draws a triangle with triangular holes at equal intervals, without lifting the pen.

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Triangles and snowflakes, continued

A Sierpiński tetrahedron seen from one corner The triangle in three dimensions. Draw four half-size pyramids, one at each corner of a large one.
Odd numbers of Pascal's triangle shaded: a Sierpiński sieve Write out Pascal's triangle and shade every odd number. The shaded cells make the fractal.
Sierpiński triangle after one cut: three corners left Split a triangle into four equal ones and remove the middle. Repeat that one move in each corner.
Sierpiński triangle at stage two: nine small triangles After the second round of cuts nine small triangles remain. Shade them and leave the four holes white.
Sierpiński triangle built by shrink and copy Shrink a triangle to half its height and width, make three copies and stand them corner to corner.
Sierpiński triangle from dots: the chaos game Pick one of three corners at random, move halfway to it and mark a dot. Keep going and it appears.

Trees and ferns 13

A Barnsley fern, each leaflet a small fern Made to resemble the black spleenwort fern from just four rules. Every leaflet copies the whole frond.
A fractal canopy turned upside down as roots The same splitting rule drawn downward from a ground line. Stop when the lines get too short to split.
A fractal canopy: every branch splits in two Split a line into two shorter lines at its end, then split those. Keep the same angle every time.
A Lichtenberg figure: one spark forking into hundreds A branching electric discharge with fractal properties. Fork every line and lighten it at each fork.
A Pythagoras tree five rounds tall The whole tree fits a box six squares wide and four squares high, measured by the first square.
A Pythagoras tree with a color for each round Color the first square, then the two on it, then the four on those. The rounds read as bands.
A Pythagoras tree: one square, two squares on top On a square build two smaller squares so that the three enclose a right triangle. Repeat on each.
A river delta drawn with the split-in-two rule Start with one wide channel and split it in two, then split each arm. Narrow the line at every split.
An H tree in three sizes of H Draw a line, then a shorter line across each end, then again. Each is shorter by the square root of 2.
An H tree packed into a whole rectangle Carried on, the H tree comes as close as you like to every point of a rectangle. Draw six sizes of H.
An L-system plant: one stem rule grown four times L-systems were introduced in 1968 by the botanist Aristid Lindenmayer to describe how plants develop.
The Barnsley fern compared with a pressed spleenwort In nature no fern quite matches another. The computed fern repeats itself exactly at every scale.
Two fractal canopies: a narrow angle and a wide one Canopies differ by the angle between branches and by how much each branch shrinks. Change one only.

Curves that fill a square 13

A Gosper curve on triangle dot paper Also called the flowsnake. Every turn is 60 or 120 degrees, so it follows triangle dot paper.
A Heighway dragon grown line by line Swap every line for two lines at a right angle, turning them right and left by turns.
A Hilbert curve shaded from one end to the other Draw the 4 by 4 step, then color along the line from light to dark to show where it begins and ends.
A Hilbert curve through a 4 by 4 grid Four small U shapes joined by three short links. Never lift the pen and never cross a line.
A Hilbert curve through an 8 by 8 grid Four copies of the 4 by 4 step, the first and last turned on their sides, joined by three links.
A Hilbert curve, first step: a square U A continuous curve that fills a square, first described by David Hilbert in 1891. Start with a U.
A Lévy C curve after four rounds Build a triangle angled 45, 90 and 45 degrees on each line and keep its two short sides.
A Moore curve: a Hilbert curve closed into a loop Four copies of a Hilbert curve joined so that the two ends meet.
A Peano curve through 81 squares Nine S shapes, each inside one square of the first step, joined end to end into a larger S.
A Sierpiński curve: a closed loop filling a square A closed curve found by Wacław Sierpiński. Its later stages fill the whole square.
A Z-order curve on a 4 by 4 grid: a Z of Zs Four small Zs, joined in the order top left, top right, bottom left, bottom right.
A Z-order curve: four cells joined by a Z Visit four cells in the order of a letter Z. Then visit four such blocks in the same Z order.
The first step of a Peano curve: an S through nine cells The first space-filling curve, found by Giuseppe Peano in 1890. Each square splits into nine.

Carpets, dusts and gaskets 13

A 2 by 2 box fractal, one corner left out Keep three squares of four, then do the same inside each. It comes close to the Sierpiński triangle.
A Cantor comb: the stages stacked as teeth Stack the stages of the Cantor set with no gap between rows, so the pieces hang down like comb teeth.
A Cantor set: a line losing its middle thirds Draw a line. Under it, draw it again without its middle third. Keep going: 1, 2, 4, 8 pieces.
A Menger sponge drawn as a cube with holes punched through Cut a cube into 27 small cubes. Remove the middle of each face and the very center, leaving 20.
A Sierpiński carpet after one cut: a square frame Cut a square into nine in a 3 by 3 grid and remove the middle one. Repeat in each of the eight left.
A Sierpiński carpet after two cuts: nine holes One large hole in the middle and eight small ones around it, each in the middle of its own square.
A Sierpiński carpet shaded as a tiled floor Draw the first cut, then tilt the square back in perspective and darken the hole like a missing tile.
A Sierpiński carpet three cuts deep, 27 cells wide Use a square 27 cells wide so that every cut lands on a grid line: holes of 9, 3 and 1 cells across.
A T-square fractal after three rounds of corner squares Draw a square. On each outer corner, center a square half as wide. Repeat on every new outer corner.
A Vicsek fractal as a plus sign of plus signs From a 3 by 3 grid keep the middle square and the four that touch its sides. Repeat in each of the five.
A Vicsek fractal as an X of Xs The other form: keep the four corner squares and the middle one, five in all, and repeat in each.
Cantor dust in two dimensions, three stages The Cantor set in more than one dimension. Keep the four corners of a 3 by 3 grid and repeat.
The fifth stage of a Cantor set: 32 specks Each stage doubles the pieces: 2, 4, 8, 16, 32. Each speck is 1/243 of the first line, so start long.

How it works

Easy fractal designs to draw, 52 of them: triangles and snowflakes, trees and ferns, curves that fill a square, and carpets, dusts and gaskets. Each hint gives the rule to repeat. The page opens on the 19 easy ones.

Read the full guide

One rule, repeated

A fractal is one small move done again inside its own result. Remove the middle of a triangle, then the middle of each triangle left. Split a branch in two, then split each branch. Two or three rounds are enough for the pattern to show.

Easy to draw fractals for beginners

Start on squared paper with the Cantor set, the Vicsek fractal or the first step of a Hilbert curve. Choose Any level under the button for all 52. Kind, under More filters, keeps the list to one group. As fractal art ideas, give each round its own color.

Use squared paper for carpets and curves, and triangle dot paper for snowflakes and the Gosper curve.

Questions and answers

What is the easiest fractal to draw?

The Cantor set: draw a line, then draw it again underneath without its middle third, and keep going. A fractal canopy, where every branch splits in two, is as easy. Easy holds 19.

How do you draw a Koch snowflake?

Start with a triangle of three equal sides. Split each side into three, raise a smaller triangle on the middle third and erase its base. Do the same on every new side. Stage one is a six-pointed star.

What is a fractal?

A shape with detailed structure at smaller and smaller scales. Many look similar at every scale, which is called self-similarity: zoom in on the edge of a Koch snowflake and the same jagged pattern appears again.

Can a curve fill a whole square?

Yes. Giuseppe Peano found the first space-filling curve in 1890, and David Hilbert described another in 1891. On paper you draw only the first few steps, through more and more cells of a grid.