THE D'CP CODE

A HOBBY OF DECISIONS

2007-02-21T11:19:00.000-08:00

INTROITO
Dear reader: I remind you that these are my notes about how am I learning everything related to the resolutions of the CPs. Pardon me for any error I commit, specially related to the pictures, the handling of the html language and the images, which I am still in process of learning its management. I learn more every day!

FIRST PART

THE MYSTERIES OF ROMAN

Some time ago, I showed 2 beautiful CPs form the Origamist (Román Díaz), and also indicated that there were big mysteries that are hidden in its lines. To begin to understand the CPs, I would like to show you one of those big mysteries. For it, click on the image that says BASE.

____

--------------CP____________________BASE----------

That’s it! One of the big mysteries hidden in between the lines of the CPs is the final model of the creator (In the last entry, Introduction and definition of CP, if you choose the other CP, the other model of Román will be revealed).
To tell the truth, the final model is there like a butterfly in its cocoon. And why do I express myself this way? It’s because it is of great importance that we understand the CPs very well, and this way we establish our proper limits for our hobby.
Usually, the CP only takes us to what we call the BASE. In the origami terminology, the base of a model is a step in the sequence of folding in which a figure is obtained with the same number, distribution and size of tips of main flaps as the final model. Sometimes, this figure will look like the final model, but generally it won’t. So to get into this wonderful hobby, which is the resolution of the CPs, we most first take away the wish to obtain with them the final model of the creator. Of course, depending of each ones skills and knowledge, many will get to the final model by means of origami techniques; but that is out of reach in this blog.
In very particular cases, we get to find origami creators that are very “kind with us” in which CPs get us very close to the final model, but that is not very common. So as said before, usually the CP takes us to the base, of some place between the base and the final model; but definitely never before the base.

I like to think of the base! I consider it as an embryo of the final model. In the CP-embryo is everything necessary of structurally important (see definition of CP in th Introductions) to obtain the final figure, but it’s always missing something more! It still has to grow, develop, define and form the details, that, by this way, finally to be born. The CPs are beautiful with its symmetries, vertices, which irradiate multiple rays, forming stars and the final model is great, with its representation; but the base, seems for me as ugly as an embryo. Many people, looking at the CP feels attracted to solve it and seeing the final model wishes to obtain it, but only a few “relatively knowing the truth” persist on wearing away their mind for the pure love towards the “ugly” embryo.

SECOND PART:

THE EASIEST CPS AND THEIR UNCERTAINTY

The two figures of origami, with the easiest CPs that exist, helps us represent mountains, volcanoes, roofs, books, doors, and thousands of things. They are of great antique and its origins are lost in the fog of the documented history. Showing them would seem trivial, but, as the inductive method shows us, the simple things helps us understand the complicated. In these two CPs are contained various fundamental concepts that will be fully used in the resolution of the CPs each time more complicated. Let’s see the CPs sketched on a square piece of paper:

(Fig. 1) CP1: Bisector_______(Fig.2) CP2: Perpendicular Bisector

The line of CP1 is denominated Bisector or Diagonal and it cuts the right angle, of the two opposite corners, exactly in angles of 45º. The figures at each side of the bisector are two isosceles right triangles, each one of them with half the area of the original square (For primary teachers, this can serve as a visual method for the teaching of geometry! This blog will contain many elements that could be useful). Let’s watch it more detailed so it gets clearer:

(Fig. 3) Divided Square _______(Fig. 4) The separated triangle

It’s a right triangle because it contains one angle of 90º, and it is isosceles since it has two equal sides.

The recognition of basic geometric figures and the mathematics concepts that rules them will be a fundamental part in the process of the resolution of the CPs. We will go little by little identifying them one by one.

By now I would just like to show you, so that you remember them, the types of triangle that exists:

(Fig. 5) Types of Triangles

Going back to the simplest CPs, figure 2 shows us the perpendicular bisector. It cuts the side of the square in two, generating two rectangles, each one with the area of the original square.

(Fig. 6) Rectangles

Now, let’s take a square piece of paper and do Origami (meaning to fold paper in Japanese). Let’s fold CP1! Then the first question we make is:

RIDDLE NO. 1
In what direction do we fold it?

I wanted to jut out this question because of its fundamental importance. The direction of the fold is the first of the great riddles in the resolution of the CPs. For each line in a CP there are only two folding options, towards (to the front) or backwards (to the back); very little, but we have to DECIDE! I call this ambiguity the FIRST SPATIAL UNCERTAINTY: the CP does not give us the certainty of the folding direction. But before we thoroughness analyze the first spatial uncertainty, we have to establish some more basic elements.

Even relatively little frequent, some origami creators show us the CP with the first riddle solved, since it shows ust the direction of each of the folds. In this case the CP is named CPMV which means CP WITH ASSIGNED MOUNTAIN AND VALLIES. Let’s watch what we refer in the easiest CPs. We are going to draw two diagonal CPMV. For that we use the symbolic notation of the origami:

(Fig. 7) CPMV: valley ________ (Fig. 8) CPMV: mountain

Then, figure seven and eight indicates us the direction of the folds, the first one a valley, and the second one a mountain. Now let’s see the diagrams of these CPMV:

(Fig. 9) Valley diagram _______ (Fig. 10) Mountain diagram

As you can see, to obtain the diagrams we just add arrows. . Now it reads like this: for figure 9 “fold the diagonal towards the front”, and for figure 10: “fold the diagonal backwards (to the back)”. Let’s do it with paper! If the paper is two color sided, we will have to consider if we want the selected color inside or outside. But for now we are not going to consider this variable and we will think the it has same color both sides.

Ok, we made it! As you can observe, for the case of single line, the direction of the fold is indifferent. Trivial for now!

Everything we have written till now serves also, and of the same way, for the CP of the perpendicular bisector. For both CPs, bisector and perpendicular bisector, and for both lines, valley or mountain, the figures obtained are shown in these diagrams:

(Fig. 11) Isosceles right triangle ___________ (Fig. 12) Rectangle

We have obtained these two basic geometric figures and I would like to indicate one more concept in the resolution to the CPs using them. If we consider the paper as a plane, we these figures are really three-dimensional, but it is common in origami to say that they are flat. So, I would like to call them MULTICAPS FLAT FIGURES, to differentiate them from the plane; but also to differentiate them from the origami figures that are really Three-dimensional, which we call 3D FIGURES

If the CPs are like the embryos of the origami models; sure the bisector or the perpendicular bisector will be the vertebral spine. They are “structurally important” lines and, for me, the first references in resolving CPs. We will dedicate to the topic of references later one. For now, we ask ourselves:

What will happen to the simplest CPs if we incorporate a new line? What variables and riddles will be proposed as challenges? Let’s have patience, that going slow get us long and sure.

Your comments are extremely important in this blog; please write them below. Don’t worry if you don’t have an account nor password, just click on anonymous, and there you can write your message.

If you wish a copy of this document in pdf format, ask me for it at eric@internetelfaro.com, that I will be glad to send it to you.

A CHRISTMAS GIFT

2006-12-29T10:56:00.000-08:00

INTROITO

Dear readers:

My blog in Spanish has four updates; however due to this special time, I decided to postpone the English version of updates till January and, instead offer you the present one. The wind brings us memory of Christmas and so I have decided to give you my CHRISTMAS GIFT. Hope you like it.

I would like to dedicate this entry to Juanjo. He joined the GOP group just a while ago; I don’t even know his real name nor his country, but the dialogue that I sustained with him in the forum of the group motivated me. Juanjo had asked for help to understand the CPs and I recommended a visit my page, to which he nicely answered: “Since I got interested in this thing about CPs, I have thought that Eric Madrigal is absolutely an eminence in this field” ("Desde que me interesé en esto de los CPs he pensando que Eric Madrigal es toda una eminencia en este campo"); phrase that I wish to answer from my blog and I do it as a way of confession, so that there is no doubt about the reality.

Juanjo thinks that I am an eminence in this matter of CPs which I must say that until today, I have only solved two CPs, one is the Elephant of Komatsu, and the other the Kiwi of Román Díaz. No more! To tell the truth, I am far away to be an eminence. If you and Juanjo read the head note of my blog, you will understand the purpose. I am learning how to solve CPs and I invite readers who wish to learn with me. My learning is meant to be slow, assimilating deeply every element, but efficiently. Clarity in assimilated ideas is the best tool to solve the jumble of rays and nuts of more complicated CPs.

If you read the entry before this one, you will notice that until now I have only studied the comet base. And that’s the reality! I am happy because when I see a complex CP, such as Alejandro Dueñas’s wolf, I am able to distinguish, in between the forest of lines, what corresponds to the comet base, even though I do not encourage collapsing it right now. Sorry!

So, you don’t have to be afraid of the CPs. We’ll get to it, slowly but efficiently, to solve the most complicated ones.

One of the consequences of a profound study of the CPs, of at least in my case, has been the motivation to create and this is the reason for this entry this 15 of December: To show you my first origami model, its CPMV an its collapsed base, so that for those who gets encouraged can make this easy but elegant model.

At last, the next entry will be published in the first days of January since it is difficult for me to update things with years-end parties.

Sincerely,

Ing. Eric Madrigal
Asociación Costarricense de Origami

1. MY FIRST ORIGAMI MODEL

WOULD YOU LIKE TO HAVE A CUP OF TEA?

Each model is made out of a foil-backed paper. The teapot is in a 25 cm x25 cm sheet of paper and both the cup and the cup with spoon are in a 12 cm x 12 cm. sheet paper. The model is not three-dimensional even though it has pockets that could contain some liquid.

About the CP of the TEAPOT, I don’t wish to do anything right now, so that you'll try to solve it. The collapsed base is also shown, and I think that you can easily get from it to the final model. I will be thankful if you could indicate me in the comments of by email if you could collapse the base, which is the original base for the references and also if you could obtain the final model. A picture will be appreciated. Many variations can be done to the final model, so with this CP you have got a lot to enjoy.

The cups are the same concept as the Teapot CP, but with slight variations. I think that those who are more advanced in origami will be able to realize this.
And so, wishing you all a HAPPY MERRY CHRISTMAS! Here is the CPMV of the TEAPOT and some other pictures of the model.

2. WITH OR WITHOUT SUGAR?

Yesterday I was very creative, so I would like to show you the last model of the series. It is recently elaborated and I had no time to take a good picture, but here I leave it with you. It is also made out of foil-backed paper of 15cm x 15 cm.

3. THANKS

I would like to show my gratitude and send an affectionate Christmas greeting to everyone that has given me their support in these months which I went into adventure in this blog.

Particularly, I wish to give thanks to José Ignacio Royo for his revision in the mathematical part of the blog.
To María José Sandí, for the effort she is making of translating this blog into French.
To Felipe Moreno who has given me the necessary incentive to keep going and the one who, since the next entry, will be the “checker” of the script.
To Elerth Leiva of Perú for his pictures and interpretations of the CPs.
To Román Diáz, Daniel Naranjo, Alejandro Dueñas for ceding me their CPs and pictures to elegantly illustrate each entry given till now.
To Diego Quevedo for his constant teaching about what is the interpretation of the CPs as well as the learning of the used software.
To Nícolas Terry for including my blog in his Web page.
To Origami Chile, Asociación Española de Origami, The Netherland Origami Association, a Gilad Aharoni's Origami Page and many more that have gladly added my link in their pages.
To the group of GOP which I belong and have put this blog in its service.
To the Asociación Costarricense de Origami
And finally to all the readers of my blog, both those that have left messages or comments and those that are completely anonymous.

FOR EVERYONE, I WISH YOU HAPPY MERRY CHRISTMAS!

In this blog, your commentaries are extremely important; please write them below. If you have neither an account nor a password, don’t worry, just click where it says anonymous (anónimo) and there you can write your message.

If you wish a copy of this document in pdf format, ask me for it at eric@internetelfaro.com that I will be glad to send it to you.

INTRODUCTION AND DEFINITION OF CP

2006-12-29T10:32:00.000-08:00

There is an Internet group dedicated to the study of the CPs called GRUPO ORIGAMI PATRONES. I belong to this group. It is the only international group whose only objective is this, and there are people who write from everywhere in the world: Colombia, Peru, Ecuador, Argentina, Brazil, Uruguay, Costa Rica, Mexico, United States, to only mention some in the Americas. But also form Spain, France, Poland, Ukraine, Thailand, Israel, and many more. What an important group! If you want to inscribe, just click on the logo:

One of the activities of GOP in the past months has been to achieve a definition for CP so that it is sufficiently clear, explicative, and in a suitable language for origamists. So, to begin this blog, we are going to define CP as the following:

CP (form the English initials for Crease Pattern), is a set of lines, sketched in a piece of paper, which indicate the location of the creases that are structurally important in an origami model; and which, folded in the directions and correct sequence are enough to get to one of the steps of the folding process, being the base or the final model, depending on the intention of the creator..

This is a deep definition that touches many elements which we will analyse in time. For now, we are going for the basics.

I got 10 different written entries, but I am going to learn a bit about diagram drawing, taking digital pictures, etc. which will allow me to illustrate the things that I am learning.

I would greatly appreciate your sending me your comments, since that would give me more material to think about. The entries will be published every 15 days.

The CPs are beautiful by themselves. For your visual delight, I will show you two samples designed by our excellent Uruguay origamist Román Días:

What mysterious secrets are to be found in between these “collections” of lines called CPs?

Your comments are extremely important in this blog, so please write them below.