Weekly Animation XXV: Compressed Soundwave

This specific pattern uses equally-spaced vertical creases. The setup is that simple, but the play comes from where the diagonals are placed. In every margin, there are three options: rising diagonal, falling diagonal, or nothing. In this case, there is a transition area of three rising diagonals in a row, followed by nothing, and then another set of three rising diagonals. At each set of rising diagonals, the reflection lines smoosh together (technical origami term).

Next week I'll post one where the set of three rising diagonals are followed by a set of three falling, and you'll see the difference.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XXV: Compressed Soundwave

This specific pattern uses equally-spaced vertical creases. The setup is that simple, but the play comes from where the diagonals are placed. In every margin, there are three options: rising diagonal, falling diagonal, or nothing. In this case, there is a transition area of three rising diagonals in a row, followed by nothing, and then another set of three rising diagonals. At each set of rising diagonals, the reflection lines smoosh together (technical origami term).

Next week I'll post one where the set of three rising diagonals are followed by a set of three falling, and you'll see the difference.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXV: Compressed Soundwave

This specific pattern uses equally-spaced vertical creases. The setup is that simple, but the play comes from where the diagonals are placed. In every margin, there are three options: rising diagonal, falling diagonal, or nothing. In this case, there is a transition area of three rising diagonals in a row, followed by nothing, and then another set of three rising diagonals. At each set of rising diagonals, the reflection lines smoosh together (technical origami term).

Next week I'll post one where the set of three rising diagonals are followed by a set of three falling, and you'll see the difference.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXV: Compressed Soundwave

This specific pattern uses equally-spaced vertical creases. The setup is that simple, but the play comes from where the diagonals are placed. In every margin, there are three options: rising diagonal, falling diagonal, or nothing. In this case, there is a transition area of three rising diagonals in a row, followed by nothing, and then another set of three rising diagonals. At each set of rising diagonals, the reflection lines smoosh together (technical origami term).

Next week I'll post one where the set of three rising diagonals are followed by a set of three falling, and you'll see the difference.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XX: Weird Soundwave

Weird Soundwave shows what happens when a reflection crease "degrades" into what I call the Zone of Transition. As a reflection line hits angle after angle of primary creases on the paper, normally it'll cross regions with the acute side of the angle on one side, and exit the region with the acute side on the other - a wordy way of saying that it zig-zags. As the angle becomes less acute (closer to right), it zig-zags less and eventually enters and exits a region where the acute angle is on the same side. What starts as an A-B zig-zag pattern has two B's in a row, and switches to a B-A pattern, and so it transitions.

The orange circles in the schematic show where this occurs. They're close enough to the edges that it doesn't make the folding much more difficult, but they do make the pattern not fully flat-foldable.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XXIV: Circular Chiaroscuro

As I understand it, Andrea Russo coined the term "chiaroscuro" when it comes to origami (as opposed to the art technique). Chiaroscuro in this case is a folding design technique that involves a sudden shift in straight lines, causing the viewer's eyes to be drawn to the shifted angle. When this is done along a shape's perimeter, it highlights that perimeter depending on the lighting. In the video below, Andrea used a square, but he experimented with many different straight-crease forms:

www.flickr.com/.../987.../38441150165/in/dateposted/

There's a massive amount to explore here, and some years ago I decided to play with circles and curved folding. I determined that "true" reflections over tangent lines was too unwieldy, and decided that the reflections don't have to go out at the same angle they entered a crease to have the same illusory effect, and started allowing them to reflect however I desired. This was one of my first tests. I have others, in a series to be posted eventually!

Check out more of Andrea's work on his flickr photostream here! www.flickr.com/photos/9874847@N03

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #chiaroscuro #AndreaRusso

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XXIV: Circular Chiaroscuro

As I understand it, Andrea Russo coined the term "chiaroscuro" when it comes to origami (as opposed to the art technique). Chiaroscuro in this case is a folding design technique that involves a sudden shift in straight lines, causing the viewer's eyes to be drawn to the shifted angle. When this is done along a shape's perimeter, it highlights that perimeter depending on the lighting. In the video below, Andrea used a square, but he experimented with many different straight-crease forms:

www.flickr.com/.../987.../38441150165/in/dateposted/

There's a massive amount to explore here, and some years ago I decided to play with circles and curved folding. I determined that "true" reflections over tangent lines was too unwieldy, and decided that the reflections don't have to go out at the same angle they entered a crease to have the same illusory effect, and started allowing them to reflect however I desired. This was one of my first tests. I have others, in a series to be posted eventually!

Check out more of Andrea's work on his flickr photostream here! www.flickr.com/photos/9874847@N03

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #chiaroscuro #AndreaRusso

Weekly Animation XXIV: Circular Chiaroscuro

As I understand it, Andrea Russo coined the term "chiaroscuro" when it comes to origami (as opposed to the art technique). Chiaroscuro in this case is a folding design technique that involves a sudden shift in straight lines, causing the viewer's eyes to be drawn to the shifted angle. When this is done along a shape's perimeter, it highlights that perimeter depending on the lighting. In the video below, Andrea used a square, but he experimented with many different straight-crease forms:

www.flickr.com/photos/9874847@N03/38441150165/in/dateposted/

There's a massive amount to explore here, and some years ago I decided to play with circles and curved folding. I determined that "true" reflections over tangent lines was too unwieldy, and decided that the reflections don't have to go out at the same angle they entered a crease to have the same illusory effect, and started allowing them to reflect however I desired. This was one of my first tests. I have others, in a series to be posted eventually!

Check out more of Andrea's work on his flickr photostream here! www.flickr.com/photos/9874847@N03

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #chiaroscuro #AndreaRusso

Weekly Animation XII: Wild Growth, folded

Considering a single region (1/4 of the paper, we'll consider the left one) as a module, this one has two collapses. The first is the set of rising parallel creases with larger and smaller margins between them in an AB pattern, creating a stairstep effect. The second is a crease that comes from the bottom and reflects over that AB pattern, bending to the right. Once you have that module, you can reflect that to the second, third, and fourth regions, and make the 1/4, 1/2, and 3/4 vertical lines the new primary collapse creases, that everything else reflects over.

I like the complexity of this approach, without it being overwhelming. As you collapse it, pieces push out and other pieces pull in, making a nice and surprising effect. Print out the crease pattern and give it a try! I also attached a few variants (painted) to show off a little of the direction this family of designs can go.

Look out for another animation on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #wildgrowth

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XXIV: Circular Chiaroscuro

As I understand it, Andrea Russo coined the term "chiaroscuro" when it comes to origami (as opposed to the art technique). Chiaroscuro in this case is a folding design technique that involves a sudden shift in straight lines, causing the viewer's eyes to be drawn to the shifted angle. When this is done along a shape's perimeter, it highlights that perimeter depending on the lighting. In the video below, Andrea used a square, but he experimented with many different straight-crease forms:

www.flickr.com/.../987.../38441150165/in/dateposted/

There's a massive amount to explore here, and some years ago I decided to play with circles and curved folding. I determined that "true" reflections over tangent lines was too unwieldy, and decided that the reflections don't have to go out at the same angle they entered a crease to have the same illusory effect, and started allowing them to reflect however I desired. This was one of my first tests. I have others, in a series to be posted eventually!

Check out more of Andrea's work on his flickr photostream here! www.flickr.com/photos/9874847@N03

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #chiaroscuro #AndreaRusso

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation VII: Mars Joker by Paulo Taborda Barreto, folded

Here's the folded form of the Barreto piece. There are actually a large number of variations in layering that you can do with this pattern, and I intend to play with them more before I put this one away.

We had our follow up discussion last Friday and explored some more of the many, many directions that Barreto takes this concept, including curved creases, rotational foldings, hinged folding patterns, and more. But this was the first "big" work in the article. I think I saw it folded once by @Tom Hull some years ago at a convention. The design starts with a zig-zag line that can be constructed arbitrarily; in this case, I traced Barreto's top edge from the book (the penultimate photo). Then, that zig-zag is rotated 90 degrees to form the left side of the model. That left side is duplicated and positioned everywhere where there is a vertex of the top zig-zag, and then finally, the top zig-zag is replicated everywhere where there is a vertex on the left zig-zag.

It lines up perfectly, but even more fascinating is that it develops an entirely flat-foldable model! There's still a lot more for me to understand from this pattern. Madonna Yoder from @Gathering Folds did a lot of narrowing down what the limits for the rotation angle are, and I think that's a solid start. I'll post more about it at some point, I'm sure!

Keep an eye out for the next animation on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MOB #MathOrigamiBeverages #Barreto #BarretoMars #marsjoker

Weekly Animation XII: Wild Growth, folded

Considering a single region (1/4 of the paper, we'll consider the left one) as a module, this one has two collapses. The first is the set of rising parallel creases with larger and smaller margins between them in an AB pattern, creating a stairstep effect. The second is a crease that comes from the bottom and reflects over that AB pattern, bending to the right. Once you have that module, you can reflect that to the second, third, and fourth regions, and make the 1/4, 1/2, and 3/4 vertical lines the new primary collapse creases, that everything else reflects over.

I like the complexity of this approach, without it being overwhelming. As you collapse it, pieces push out and other pieces pull in, making a nice and surprising effect. Print out the crease pattern and give it a try! I also attached a few variants (painted) to show off a little of the direction this family of designs can go.

Look out for another animation on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #wildgrowth

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XIV: Saw Tooth Corrugation, folded

The way this works is by having pairs of alternating nonparallel creases that reflect over the horizontal lines, an A-B angular pattern. The alternating angle becomes a bend when the model is collapsed. If two creases (one mountain and one valley) are at a particular angle theta, the strip will bend 2*theta off of being straight when folded.

This happens each time there's an alternation, and you can specify particular bend angles as you like. For example, if you wanted to make a hexagon, you'd need 120 degree bends. 180-120 = 60, so you'd need 30 degree angles on the crease pattern (60/2).

At either end of the "sawblade", I skip a reflection line, and end up bringing the plane back to its original orientation, effectively flat. See schematic picture for a visual diagram of this. Truth be said, I think these are a little more than half circles. I could sit down and truly get flat extensions between the sawblades, but maybe that's a project for some time down the road.

Another animation to come on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #Sawtooh

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XVI: Hilbert Curve, WBT Version

One of my first origami studies was on the traditional waterbomb base, and variants of it. It's got a large overlap with the Fold-and-Cut problem. In my case, it was just folding, and I used the fold lines to sink folded vertices in and out as much as I wanted. erikdemaine.org/foldcut/

This can extend to open-ended curves as well as enclosed shapes. This is a "waterbombed" solution for the Hilbert curve. Next week, I've got another origami interpretation of the third order Hilbert Curve, so keep an eye out for that!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #chiaroscuro #Waves #Hilbertcurve

Weekly Animation XII: Wild Growth, folded

Considering a single region (1/4 of the paper, we'll consider the left one) as a module, this one has two collapses. The first is the set of rising parallel creases with larger and smaller margins between them in an AB pattern, creating a stairstep effect. The second is a crease that comes from the bottom and reflects over that AB pattern, bending to the right. Once you have that module, you can reflect that to the second, third, and fourth regions, and make the 1/4, 1/2, and 3/4 vertical lines the new primary collapse creases, that everything else reflects over.

I like the complexity of this approach, without it being overwhelming. As you collapse it, pieces push out and other pieces pull in, making a nice and surprising effect. Print out the crease pattern and give it a try! I also attached a few variants (painted) to show off a little of the direction this family of designs can go.

Look out for another animation on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #wildgrowth

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XIX: Spiral Tubes

It's a poorly kept secret that I'm working with origami spiral designs a lot these days. I find them most interesting when they spiral around the center several times, but many of the results end up spiraling out to infinity pretty quickly, depending on the angular spacing between the creases.

Here's a cool use for them, though! This pattern involves a rapidly accellerating spiral, which is mirrored. It's sort of drowned out by the bolder tube shape that emerges, but it's still visible in the underlying design. I think it looks kinda cool, and I'd be interested to see if there are other origami forms that naturally cause the paper to bend like this!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XXIII: Radiate and Oriedita Exploration

The radiate pattern is a pretty simple one, but can be used as the groundwork for more complex and interesting designs. Even still, by itself with the right lighting it looks neat; those shadows really pop!

I'm at the OrigamiUSA convention in Manhattan this weekend, and learned about a sweet origami design software called oriedita. In my playing with it I'm finding huge potential to decrease the time I take on my corrugation designs. To date, I've been using Inkscape - an incredible program - but my reflection-and-extend/retract method of designing is not really what Inkscape is meant for. Oriedita should help with that aspect significantly, as it's a CAD program that's for origami designs.

I've thrown in some explorations with the program and the Radiate pattern after the crease pattern. These were quick; I think I did all of the designs and photos exports in about fifteen minutes... crazy. There's a wide playground available, and I'm excited to explore it more!

Special shout-out to Bodo Haag (ko-fi.com/bodorigami, @bodo_ori on Instagram) - one of the invited guests at the OUSA convention - for introducing me to oriedita and walking me through some of the basics.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves # oriedita #OUSA #OrigamiUSA #OUSAConvention2023

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XIV: Saw Tooth Corrugation, folded

The way this works is by having pairs of alternating nonparallel creases that reflect over the horizontal lines, an A-B angular pattern. The alternating angle becomes a bend when the model is collapsed. If two creases (one mountain and one valley) are at a particular angle theta, the strip will bend 2*theta off of being straight when folded.

This happens each time there's an alternation, and you can specify particular bend angles as you like. For example, if you wanted to make a hexagon, you'd need 120 degree bends. 180-120 = 60, so you'd need 30 degree angles on the crease pattern (60/2).

At either end of the "sawblade", I skip a reflection line, and end up bringing the plane back to its original orientation, effectively flat. See schematic picture for a visual diagram of this. Truth be said, I think these are a little more than half circles. I could sit down and truly get flat extensions between the sawblades, but maybe that's a project for some time down the road.

Another animation to come on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #Sawtooh

Weekly Animation X: Splitter Series, Excerpts

So the way I design these is I start with a straight vertical line. Then I reflect another crease over it, creating a V shape. Then a third crease that hits the second a little lower than the intersection, which reflects through the other lines, coming out the other side, making a wider V. With each iteration, the V gets wider and wider, lower and lower, until you get this neat curve.

Now, the amount of distance from the previous intersection that a new hits the previous one is based on a set percentage of the previous crease to the edge of the paper (7/8 of the way up), which means that the edge of the paper actually drives this design significantly. After several iterations, the reflect creases curl into each other and create a splitting effect. Maybe that series will be one of the next few patterns :)

But for now, enjoy the thought experiment, and keep an eye out for the next pattern on Friday!

#origami #corrugation #artwork #paper #folding #math

#benparkerstudio #MiuraOri #splitterseries

Weekly Animation XXI: Penta Spiral

So how does a spiral have radial symmetry? Well, it's actually five spirals that rotate around each other. Like the others of my spiral series, this one patterns the circle with an oscillation between a large and small angle (46 degrees and 26 degrees), back and forth, and this drives a reflection crease to create a spiral - in this case, one with a quick acceleration. There's enough space between the creases to allow another to fit in rotated 72 degrees using the same radials... and another, and another, and still one last one.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MakerspaceCT #Waves #spiral #spirals

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XVII: Hilbert Curve, Chiaroscuro Version

You can really see the outline of the Hilbert curve through the folding. It's a fun one to fold, and I might develop it at some point and do a fourth order pattern soon!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #AndreaRusso #chiaroscuro #Waves #Hilbertcurve

Weekly Animation XV: 11/9 Owlified, folded

You can see in the schematics photo (toward the end) how this was generated, "elastic band" around the spiral, mirrored, and then the radials that create the outer border. The border is a variant of @Andrea Russo's chiaroscuro technique. Redirecting the creases that hit a boundary focuses the eyes on where the intersections are. I've got further studies in that vein that I'd like to post at some point too, but maybe that'll be next week's post!

Keep an eye out for Friday's animation!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #owlification #Waves

Weekly Animation XXII: Flower Hendecagonal Star

A few months ago (17 weeks, my social media is telling me), I posted the Hendecagonal Star. This takes it down a fractal path by embedding one in another in a third, each one scaled up with regard to the the previous. What results is a bowling effect that looks quite nice.

And like last time, see if you can spot the irregularity - this has bilateral symmetry, but not radial symmetry.

Friday I'll post the next one!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves #hendecagon

Weekly Animation XVIII: Fine Threads

The fine threads pattern shows that a good combination of wide and thin margins create these dramatic bold elements in the pattern. Thin margins between adjacent creases draw the viewer to their paths with strong shadow contrast. It's a fun challenge to do by hand (though I used a scoring machine for this one).

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XIX: Spiral Tubes

It's a poorly kept secret that I'm working with origami spiral designs a lot these days. I find them most interesting when they spiral around the center several times, but many of the results end up spiraling out to infinity pretty quickly, depending on the angular spacing between the creases.

Here's a cool use for them, though! This pattern involves a rapidly accellerating spiral, which is mirrored. It's sort of drowned out by the bolder tube shape that emerges, but it's still visible in the underlying design. I think it looks kinda cool, and I'd be interested to see if there are other origami forms that naturally cause the paper to bend like this!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XIII: Pyramid Steps, Folded

This one has a diagonal valley fold, and relatively close pairs of mountain-valley steps that reflect over the diagonal. This creates a stairstep pattern. Cool thing about folding a stairstep pattern is that - assuming the proportions are just right - the paper is only at most three layers thick at, so this is pretty simple to fold freehand.

After the stairstep pattern is created, cross creases that follow the other diagonal reflect and form the "ripples", and the whole thing folds flat. This one has a fair number of different ways it can be morphed and sculpted, or you can display it in its resting state like in the yellow image attached.

www.benparkerstudio.com/waves---2018.html

I'll post another on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #pyramidsteps

Weekly Animation XX: Weird Soundwave

Weird Soundwave shows what happens when a reflection crease "degrades" into what I call the Zone of Transition. As a reflection line hits angle after angle of primary creases on the paper, normally it'll cross regions with the acute side of the angle on one side, and exit the region with the acute side on the other - a wordy way of saying that it zig-zags. As the angle becomes less acute (closer to right), it zig-zags less and eventually enters and exits a region where the acute angle is on the same side. What starts as an A-B zig-zag pattern has two B's in a row, and switches to a B-A pattern, and so it transitions.

The orange circles in the schematic show where this occurs. They're close enough to the edges that it doesn't make the folding much more difficult, but they do make the pattern not fully flat-foldable.

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #origamisimulator #Waves

Weekly Animation XIV: Saw Tooth Corrugation, folded

The way this works is by having pairs of alternating nonparallel creases that reflect over the horizontal lines, an A-B angular pattern. The alternating angle becomes a bend when the model is collapsed. If two creases (one mountain and one valley) are at a particular angle theta, the strip will bend 2*theta off of being straight when folded.

This happens each time there's an alternation, and you can specify particular bend angles as you like. For example, if you wanted to make a hexagon, you'd need 120 degree bends. 180-120 = 60, so you'd need 30 degree angles on the crease pattern (60/2).

At either end of the "sawblade", I skip a reflection line, and end up bringing the plane back to its original orientation, effectively flat. See schematic picture for a visual diagram of this. Truth be said, I think these are a little more than half circles. I could sit down and truly get flat extensions between the sawblades, but maybe that's a project for some time down the road.

Another animation to come on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #Sawtooh

Weekly Animation XIV: Saw Tooth Corrugation, folded

The way this works is by having pairs of alternating nonparallel creases that reflect over the horizontal lines, an A-B angular pattern. The alternating angle becomes a bend when the model is collapsed. If two creases (one mountain and one valley) are at a particular angle theta, the strip will bend 2*theta off of being straight when folded.

This happens each time there's an alternation, and you can specify particular bend angles as you like. For example, if you wanted to make a hexagon, you'd need 120 degree bends. 180-120 = 60, so you'd need 30 degree angles on the crease pattern (60/2).

At either end of the "sawblade", I skip a reflection line, and end up bringing the plane back to its original orientation, effectively flat. See schematic picture for a visual diagram of this. Truth be said, I think these are a little more than half circles. I could sit down and truly get flat extensions between the sawblades, but maybe that's a project for some time down the road.

Another animation to come on Friday!

#origami #corrugation #artwork #paper #folding #math #benparkerstudio #MiuraOri #Waves #Sawtooh

Weekly Animation IV, folded

Here's Friday's folded piece! On my personal list of things is to turn this into a functional bowl at some point, but that's a later project.

You can see in the middle how chaotic the fold facets get and at some point you just have to give up and let the surrounding geometry hold the thing in place. This is on my list of concepts to do a video essay about. Keep an eye out for that :)

#origami #corrugation #artwork #paper #folding #math

#mathisfun #benparkerstudio #yoshimuraorigami

Weekly Animation X: Splitter Series, Excerpts

So the way I design these is I start with a straight vertical line. Then I reflect another crease over it, creating a V shape. Then a third crease that hits the second a little lower than the intersection, which reflects through the other lines, coming out the other side, making a wider V. With each iteration, the V gets wider and wider, lower and lower, until you get this neat curve.

Now, the amount of distance from the previous intersection that a new hits the previous one is based on a set percentage of the previous crease to the edge of the paper (7/8 of the way up), which means that the edge of the paper actually drives this design significantly. After several iterations, the reflect creases curl into each other and create a splitting effect. Maybe that series will be one of the next few patterns :)

But for now, enjoy the thought experiment, and keep an eye out for the next pattern on Friday!

#origami #corrugation #artwork #paper #folding #math

#benparkerstudio #MiuraOri #splitterseries

Pod Piece, Folded

This is the folded form of Weekly Animation II, the Pod Piece. I decided I wanted to test out my airbrush on the finished form with this one and I absolutely love the effect! The color is Musou black, which is supposed to absorb 99.4% of light. I think I just needed more coats to get close to that effect, but I think it looks pretty slick as-is.

More animations and prints to come this Friday!

#mathisfun #origami #folding #origamisimulator #corrugation #artwork #paper #math #animation #benparkerstudio