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For other uses, see Zig zag.From the point of view of symmetry, a regular zigzag can be generated from a simple motif like a line segment by repeated application of a glide reflection.The Treasury (also Treasure Island) each had a distinct zigzag roof, many of which still survive on reused buildings nearly three decades after the chain closed.The roof zigzag was also seen on the store logo.This would not make the trip any shorter; however, it might avoid traffic.The trace of a triangle wave or a sawtooth wave is a zigzag.Pinking shears are designed to cut cloth or paper with a zigzag edge, to lessen fraying.In sewing, a zigzag stitch is a machine stitch in a zigzag pattern.Tightly spaced zigzag stitches are used to emulate embroidery stitches such as satin stitch, and to reinforce buttonholes.This is done when another panel will overlay the seam and provide support.This page was last modified on 2 April 2008, at 22:27.Cast overview, first billed only) John Leguizamo ...Goofs:
Continuity: The length of Singer's cigarette when he is in the hospital with Jenna.Quotes:
ZigZag:
The sun is full bright today.And the tires are alive because the streets are covered with little pools that explode.The sounds and the smells and different people, all crashing down together.So loud they go invisible, silent.Just floating around like ghosts.Thank you, your vote will be counted and appear on this page within 24 hours.ZigZag is the main character in this film, he is a young
autistic boy with an abusive, junkie father.ZigZag finds peace and a
father figure in John Liguzamo's character who is his big brother.The
realtionship between the two is a match made in heaven.All in all, a great touching movie!Terms and Privacy Policy under which this service is provided to you.This document provides a short introduction to the abstract ZigZag
structure and gives some pointers for designing structures for various
applitudes.Unlike most of the other documentation related to GZigZag,
this document is more about the abstract structure, not this one particular
implementation.CSS version exists: you can try by compiling this
document from its WML version with some switches..However, I like
the pretty rendering by Mozilla so much that that's still the default.Introduction
The best words I've heard to describe the ZigZag structure
are "hyperstructure kit".The purpose of this document is to introduce
the reader to the ZigZag structure and some example applications of
it.See also the glossary of ZigZag terminology in XXX.In UNIX (at least originally), everything
is a file.ZigZag is quite similar: everything is a cell and
connections between the cells.However, the structure set up by ZigZag is
far richer than a hierarchical file system, allowing more interconnectivity
between related information.The cells are the primitives of the structure and the structure is formed
by connecting cells to each other through dimensions.All kinds
of structures are possible: loops, spheres, trees etc.The kind of structure to choose for your application is up to your
imagination.However, locally, from the perspective of one or two cells, this will
still look like the spreadsheet: each cell has its neighbours and
you go from it to one direction and then turn around and come back in
the opposite direction, you end up in the same cell.Another place to look for good, related visualizations, is the work
of M.Escher, who has created many paradoxical spaces that would fit
well with ZigZag.That is, instead of considering cells and connections, consider lists (each
list labeled with a string) of
cells where the same cell may be on several lists (but only one
with any given label).As an example of such a structure, consider a list of people and their
birth years.It'd be quite natural to have first names, last names and
birth years in their own columns, each row being one person.Also, it would then be easy to select subsets of the people on other dimensions,
for example for people who are currently in the same class or whatever.Comparing ZigZag with existing computer structures.To put it coarsely, outside ZigZag there are three different kinds of
structures in computers today: linear lists (and grids i.That is really messes, not meshes.At first it may seem strange that a structure that restricts the
number of connections from each cell can be generic but this simple
restriction is what brings about the coherence of ZigZag.You can always find which cells refer to a given cell.One interesting thing to note
about ZigZag and existing structures,
the importance of which I really only realized while doing a demo at Nokia
is simply that by using different dimensions, ZigZag allows you to
arrange the same things into different traditional
structures.So you can have the same cells in a tree along two
dimensions (as you'll see below, trees are easiest done using two
dimensions, one to go from the parent to the first child and the other
to move along siblings), a list along another dimension and a table
along two other dimensions.If you use relcells (see below)
you can even put the same things (this time, not cells: you do have to do a step of indirection)
into different structures along the
same dimensions.Viewing
Now that the structure is defined, we have to be able to view and edit
it on the computer somehow.Of course, we could just put this
structure in a text file and edit it by naming cells with numbers and
links by naming the cell numbers but this would lose the visuality
inherent in the design.There are many variations to the theme of viewing
ZigZag structures.Specific views are related to applitudes, explained below
in more detail.In this section, we look at the structure of several generic views.Before going to the views themselves, let us first define some terms:
the raster and the view.In order to look clear to the human observer, visual cues about the
structure are vital.All neighbouring cells that lie next to each other
should be connected with a line, and all cells that have neighbours
that were not displayed because of the raster should have e.Even here, there are many different possible
rasters for choosing which cells to place where, since
a general ZigZag structure will not fit a rectangular grid
and parts have to be clipped out.The two simplest rasters useful for the rectangular views
are the row and column rasters, which are actually
the same raster but placed on the screen rotated 90 degrees
from each other.These rasters are called hard rasters:
the arrangement of cells is fixed so that there is
only one possible path from the cursor to a cell to be
placed in a given position on the screen.The point of soft rasters is that since ZigZag structures are
often relatively sparse in terms of connections, the
hard row and column rasters may show relatively few cells at
a time.Soft rasters are able to show more of the structure
at the same time.These cells are then placed on screen starting with the center
cell and reducing the cell size as the distance from the cursor
grows.This causes cells that would be in the same slot
in the rectangular grid to be plotted apart from each other.The previous views have dealt with a few dimensions but several
steps along those dimensions.Applitudes
To distinguish itself from the traditional, monolithic applications,
ZigZag uses the term applitude for a "zone of functionality".The difference between applications and applitudes is the interconnectivity:
whereas conventional, monolithic applications are used to having all data
in their own files, applitudes can easily share cells and simply use
their own, orthogonal dimensions to connect cells.Everything connected to a particular person, for example, is
connected to the same cell, whether in the email applitude, the calendar,
the collection of documents or anything.Designing structures
In this section, we'll go through some commonly occurring
structural patterns in ZigZag.The patterns here are not formalized as far as OO design patterns
but carrying out such a treatment would not be difficult.Single cells and single connections are building
blocks, not necessarily complete entities by themselves.One of the basic structural mechanisms in ZigZag is
cloning, i.This mechanism is coupled with the cell content:
the contents of all clones is the same as the contents
of the root clone, and editing a clone edits the root clone.The reason is that then this dimension would always lead
to predictable structure and the applitude could
easily give interesting visualizations of the meetings
a person participated or will participate in.This is a fairly unsettled question.With more experience
in designing different applitudes we will be able to tell easier when
clones are appropriate and when special dimensions are better.Sometimes, there is a good, unique way of arranging cells along a
dimension, e.However, sometimes there is not,
or there are two different orders you'd like to have.Another alternative (that does not currently work) will be
to thread the cells through several dimensions, most of which
are implicit: for example, an implicit d.Even though the structure only allows only
two connections along each dimension, it
is possible for
many cells to refer to one in ZigZag.There are of course
different ways for creating many to one reference,
but two main ones distinguish themselves.If the referents can be of the same "type", then
it becomes necessary to allow the cell referred to to
refer to another cell.In such case, a construction called
a corner list is used.This would make a tree mapped as in the figure XXX.It is good to remember that the same cells can be in
several different trees using different dimensions.However, this is a fairly untypical example.This way, each cell can have the same relationship to
several other cells at the same time.Changing the ordering of siblings in a corner list,
with and without structural cell.For example, it provides (XXX image) a good reason to use
blank cells in corner lists for separating the parent
and sibling relationships.Merging in this change with the
blank cell is straightforward: it is simply changing the arrangement
of a single rank, with the headcell remaining in place.The existence of this "problem" is fairly natural.As every object (structure)
has its own invariants, the only thing we can assume in general is
a permanent identity cell.However, I don't understand where you go from
here: I would simply conclude here that identity cells
are a good idea...Referrals to "the list this cell is on along dim x", or "the cell
three cells posward on d.What would an identity cell for the first of these referrals be,
if there were one?That would of course be the list itself, but it
is not a "list with this particular cell", it is just a list.Thus
the target of referral does not exist in the structure.Using a space part for the connection
is possible only if space parts are allowed to manage connections
along "normal" dimensions between two possibly normal cells.Space parts can also be used to define new structures
based on a space, iff there is a surjection from the valid
states of the space to the valid space part states.If
the space part is to be writable (user can change from any
valid space part state to any other), the surjection must
also be an injection.Note that any connections to space part
cells are part of the space, and such connections are very
likely to reduce the number of valid space states due to
unpredictably changing space part cell id's.There is no good way to pick just one way to represent
the information since the idea "B is A's cousin" is perfectly
valid, even without knowing whether it is on the mother's or
father's side.From the 100K Competition, Deshpande Center, Enterprise Forum, Venture Mentoring Service and more, see how students, faculty, and alumni are part of the ecosystem.Along the way, play soccer in the middle of a Brazilian highway.Find out how alumni continue to make MIT a part of their lives.Catch a glimpse of the MIT freshman experience.Ethanol boosted gasoline engine, FAT Chain Reaction, IAP.Class of 2010 Portrait, 2006 Biobash, Student Activites Midway, Firetruck Hack.ZigZag is a production of MIT Academic Media Production Services.ON
Adam Moore has kindly set up a demo showing the royal families of
Europe in zzstructure.Walk through it on your Mac or PC.Put it in Windows C: or on Mac Desktop.The title is "A
Cosmology for a Different Computer Universe: Data Model, Mechanisms, Virtual
Machine and Visualization Infrastructure".Other previous versions (Azz, Ezz, Zzz and Mantra Server) are of theoretical
and historical interest but we don't have time to explain them right now.THE MOST GENERAL DATA STRUCTURE?That structure we call zzstructure, or hyperthogonal structure.Hyperthogonal structure adheres to no formal model anybody
knows.Just as a spreadsheet adds views
and operations to a 2D table, allowing you to see and manipulate it, ZigZag
adds views, operations and animations to hyperthogonal structure, allowing
you to see and manipulate its rich possibilities.Our logo says it all:
locally rational,
globally paradoxical,
yet somehow comprehensible.
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