Transum Software

Fractal Mosaic

Follow the precise instructions to create the ever-growing fractal mosaic pattern.

Click all the empty squares that touch the red square along one side only.

Animated version | Alternative animated version

Instructions

This is an exercise in following very precise instructions. Click on the squares in the grid above that touch a coloured square along one side only as stated in the message at the top of the page.

After four squares have been clicked a "Check" button appears that you should use when you think you have finished a stage of the pattern. The message at the top of the page will then change telling you what to do next.

When your pattern has grown to fill the grid you will be awarded a Transum Trophy for your efforts.

This pattern is a basic example of a fractal, a design produced by repeating the same set of rules repeatedly. You could produce this pattern on squared paper using crayons and extend the pattern so that is becomes huge. Please send Transum a photograph of your completed fractal.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Newsletter

Newsletter

The Transum Newsletter for April 2025 has just been published. Click on the image above to read about the latest developments on this site and try to solve the puzzle of the month. You can read the newsletter online or listen to it by downloading the podcast.

Answers

A finished version of this pattern is available to those who have a Transum Subscription and are signed in.

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Transum,

Tuesday, August 25, 2015

"The finished designs provide great displays for your classroom. Try using different colours to vary the pattern. You can find instructions to display on the whiteboard on the Snowflake Squares page."

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Transum.org is a proud supporter of the kidSAFE Seal Program

Example

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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