30 unique tiles from a set of 105. The remaining 75 tiles can be formed by rotating and/or reflecting one of the 30. The enquiry started following a social media discussion about uniqueness.

That there are 105 possibilities was proven via some simple maths. Initially, with 8 points, when deciding how to connect the first point to another there are 7 possibilities. With 2 points now occupied, 6 remain. So, when deciding how to connect the third point to another there are 5 possibilities. Continuing this until all the points have been used in a connection we get: 7 x 5 x 3 x 1 possibilities = 105. The rotation and/or reflections were eliminated by visually checking each of the 105 against each other. This could have been done via a computer programme, but as one-off exercise the visual method was sufficient.

However, a Processing sketch was used to make the drawn outcomes. This allowed for many tweaks in relative dimensions and use of colour (or not as here). There are other outcomes from or related to the idea and I will add to this archive post as time permits.

a random shifting grid of the 30 tiles / REVAD.COM #ARTbyrevad © revad

30 unique connective tiles as a grid

a fixed grid of the 30 tiles / REVAD.COM #ARTbyrevad © revad