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Square Snowflake
Striptease
Surface Tension
Swirl Without End
Take Five
The Woolsack
Tilting at Windmills
Tower Blocks
Try Angulate
Under Orders
Wall Chart
Walls of Troy
Wheels Within Wheels
Wheely Colourful
Window Boxes
Windows 100
Wreck Tangled
End of Afghans

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Home
About Turn
Amazement
A New Angle
AO
Backgammon
Basketweave
Best of Both Whirls
Bifocal
Bunch of Fives
Cable Tube Map
Chartres
Checkmate
Chromatic Scale
Code Comfort
Counting Pane
Cubism
Curve of Pursuit
Data Log
Dodecagon Thing
Doing the Rounds
Double Base
Double Vision
Equal Parts
Fibo-optic
Fibrenacci
Figure of Eight
Finite Field
Flatland Lock
From Square to Eternity
Four Corners
Give Me a Clew
Going Underground
Golden Spiral
Granny's Draughtboard
Granny's Ludo
Half Measures
Have It All Ways
Key Rings
Long and Winding Road
Lucas Like Fibonacci
Making Waves
Mere Bagatelle
Metafourmosis
Mixed Mitrefours
Money Spinner
Noughts and Crosses
Order of Magnitude
Over and Out
Penrose
Pieces of Eight
Place Order
Points of Departure
Point to Point
Pseudoku - Crochet
Pseudoku - Knit
Pythagoras Tree
Pythagorean Ripples
Revolution
Ring-road
Rule of Three
Run Rings Round
Scaled Up
Snakes and Ladders
Some Square Over The Rainbow
Spacecraft
Spaghetti Junction Map
Spinning a Yarn
Square Deal
Square Deal Redux
Square Deal Reformation
Square Root
Square Snowflake
Striptease
Surface Tension
Swirl Without End
Take Five
The Woolsack
Tilting at Windmills
Tower Blocks
Try Angulate
Under Orders
Wall Chart
Walls of Troy
Wheels Within Wheels
Wheely Colourful
Window Boxes
Windows 100
Wreck Tangled
End of Afghans

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SQUARE SNOWFLAKE

A representation of a ‘space-filling curve’.

There are several curves similar to this. Technically, this is a Sierpinski Closed Peano Curve. Giuseppe Peano was the first to describe this type of curve. Waclaw Sierpinski used his ideas to generate a curve with no beginning and no end.

Theoretically these curves cover every point on the surface until nothing is left. This can be imagined in mathematical theory but does not work in real life.

Scroll down for more information about

Square Snowflake

CONSTRUCTION INFORMATION

The background is worked as a filet crochet grid. It is important that the squares should be square. The pattern gives various ways to achieve that.

The curve is attached to the grid by surface crochet. It is an easy technique but needs a lot of concentration.

CROCHET INFORMATION

The filet crochet background is a 64 x 64 grid. It is best worked in a smooth yarn.

The curve can be added with any thicker yarn.

This is a very light and airy afghan, which could also be doubled over and used as a shawl.

Spacecraft is on a 64 x 64 grid. The examples given here are on a 16 x 16 grid to show how the principle works.

Stage 1

Imagine the grid divided into four squares. The curve takes the same shape through each of those squares.

Stage 2

Each of the four large squares can be divided into four more squares. The curve passes through each of these squares in the same way.

Stage 3

The squares are subdivided into four again and the curve follows the same path around these.

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larger pictures