How to draw FOCI

Hello friends and a very happy Friday to ya …

Today we have another fun tangle explore from Alexandra Wright who recently shared her Cutzag tangle with us. Foci has many possibilities, as you’ll see shortly.

In this notecard, Alexandra combines Foci with CZT Tomàs Padrós’s Folium and Jem Miller’s Snag.

Alexandra explains the inspiration for her Foci tangle and how she developed the variations:

Foci was inspired by an animation I remember my calculus teacher showing us when I was a senior in high school. The animation showed a point traveling along the curve of an ellipse while two lines, connecting the point to each foci (plural for focus), lengthened and shortened as they followed the point. The ellipse is one of the four conic sections learned in math: circle, ellipse, parabola, hyperbola.

Its common name is an oval, but it is so much more than just an oval! Ellipses have two foci, as compared to the circle, which only has one focus (also called the center). On a true ellipse, if you measure the distance between a point on the ellipse and the two foci and add those distances together, the sum remains constant. The animation my class watched was showcasing this concept.

My memories of the animation helped me to first create Foci. I connected each point along a curve (imagine that curve as being part of an oval) to two foci beneath the curve. The end result had a fun kaleidoscope-like feel to it. Then, I told my math brain to take a backseat, and I started to change the number and arrangement of the foci (step one) and/or the number and arrangement of the remaining dots (step two). Untold variations were born!

I don’t always have tiles, but as a teacher, notecards are readily available. I decided to tangle Betweed on the back of this notecard, and then I tangled Foci in between each gap around.

For my example of Foci, I simply added dots at the base of the arc of dots in Alexandra’s Step 2 so that the dots in Step 1 were above than the bottom ones. Also stretched out the arc considerably.

Alexandra illustrates the step-by-step instructions for drawing Foci below where she features it in a tile with the Zentangle-originals Echoism and Knightsbridge.

Image copyright the artist and used with permission, ALL RIGHTS RESERVED. These images are for your personal offline reference only. Please feel free to refer to the images to recreate this tangle in your personal Zentangles and ZIAs. However the artist and TanglePatterns.com reserve all rights to the images and they must not be publicly pinned, altered, reproduced or republished. (Small side note: if you look at the legalese in Pinterest, you are legally responsible for obtaining permission to post every photo that gets ‘Pinned’. Giving credit or sharing the source link doesn’t count.) Thank you for respecting these rights. “We must all face the choice between what is right and what is easy.” ~ Albus Dumbledore

Alexandra includes this note with her illustration of Foci variations for us to explore:

Simply by playing around with steps one and two, you never know what this tangle will look like. My page of variations is literally only the tip of the iceberg. I hope that everyone enjoys using this simple-to-do but amazingly diverse tangle. I have yet to find an arrangement of dots that does not yield a fun-to-look-at final result.

Image copyright the artist and used with permission, ALL RIGHTS RESERVED. These images are for your personal offline reference only. Please feel free to refer to the images to recreate this tangle in your personal Zentangles and ZIAs. However the artist and TanglePatterns.com reserve all rights to the images and they must not be publicly pinned, altered, reproduced or republished. (Small side note: if you look at the legalese in Pinterest, you are legally responsible for obtaining permission to post every photo that gets ‘Pinned’. Giving credit or sharing the source link doesn’t count.) Thank you for respecting these rights. “We must all face the choice between what is right and what is easy.” ~ Albus Dumbledore

As you enjoy any of the tangles on the site, please leave a comment of thanks and encouragement to show the artists you appreciate them for sharing their creativity to inspire yours. Your thanks helps motivate them to continue to share! And please share a link to your favorite tangles on social media. Thanks!

Check out the tag alexandraw for more of Alexandra’s tangles on TanglePatterns.com.

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5. Linda's List of Zentangle-Original Patterns — here is the complete list of original tangles (aka "official tangles") created and introduced by founders Rick Roberts and Maria Thomas, including those not published online. If you are new to the Zentangle Method I highly recommend learning a few of the published Zentangle classics first.
6. "A Zentangle has no up or down and is not a picture of something, so you have no worries about whether you can draw a hand, or a duck. You always succeed in creating a Zentangle." Thus patterns that are drawings of a recognizable naturalistic or actual object, figure, or scene, are not tangles. A pattern is not always a tangle — here's what makes a tangle. TIP: tangles never start with pencil planning.
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