Sierpinski Gasket L5 Photo Diagram and Design scheme note

Kei Morisue / 森末　圭 / 森　魔鬼

2023年7月26日 09:17

Gellary

Example work by Noah Konopny (IG: @ noah_konopny) from 60cm hexagon craft paper

Example work by Kei Morisue from 70cm hexagon shadow fold (painted)

Example work used in the diagram from 78cm hexagon Kami

Crese Pattern

3^3=27th grid on each edge of the hexagon

Cp drawn with help by Avinash Kanik @origamifaust

Design Scheme: RPEC

basical idea is founded on "Paper Edge Calculation" (PEC) deeply/kindly instructed below:

Just by following this idea, one could also make the Gasket L5 (old version):

LHS: currenct version, RHS: old version See how much thicker the old version is.

You can see that lots of areas inside the paper is wasted due to looong contour of the color changing borders:

The old version covers all the color borders by the edge of the paper

Instead the current version applies Reduced PEC (RPEC), covers less borders.

The current version covers the borders only shorter ones to save the size of the rerqired paper. Note that 4*3+2*6+1*6=30 units of the border are "reducted".

PEC focuses only on the edge of the paper, while RPEC utilizes both edge and flaps to reduce the grid.
RPEC is basically PEC, so it obeys single rule as PEC but also has another 2 rules:
1. (PEC) paper edge becomes color borders.
2. (RPEC1) flaps hide (immune) the color borders in 1.
3. (RPEC2) the edges(except the "root") of the flaps also become color borders.

Greens are flaps (the circles are the tip of them) and are designed to "immune" the unnnecessary borders. And at the same time, they make the rest of color borders that are not covered by PEC.

One can easily manage how to build a flap by the "circle packing method":

It is not that much trivial to design the flaps in desired location/direction(i.e. the "roots").
Also RPEC has to be "balanced" both making larger flaps (i.e. larger size of the paper) and saving the length of the contour (i.e. less size of the paper). Namely, too much RPEC cannot afford flaps to cover omitted borders. Thus there had to be trials (put RPEC at certasin reduction) and errors (find it theres no sufficient areas to make the flaps) to find the final solution (i.e. the current version).

Diagram

The diagram contains 21 steps of "Digital" diagram and following 130 "photo" diagrams.
120 of the photoes are premium.
All photoes do not have any descriptions nor instructional symbols on it. Please check the style in the steps 22~33.