Find Arrangements of Polylines in Squares

Tzu-Chieh Kurt Hong
03/01/2019

This example shows how Shape Machine is able to access any part of a shape even though the part is not registered in the database of a CAD system (in this example: Rhinoceros 5.0). By applying various shape rules the Shape Machine can also modify the parts found according to the rule that users designed. This video showcases how an initial model consisting of two squares drawn in two alternative ways can be queried and restructured in a number of different polygons under different transformations. The first example shows how a pictorial query of triangles drawn on top of the initial model restructures the model in four triangles. The second example how a pictorial query of pentagons drawn on top of the initial model identifies four isometric pentagons in the model. If the query is extended for any type of pentagons, then the shape machine is able to find twelve pentagons as topological transformations of the initial drawn pentagon. Reversing the argument, the shape machine can find two topological transforms of a paper-napkin hexagon.

The second part of the video shows how Shape Machine is able to access arrangements of subshapes within a shape even though these parts are not registered in the database of a CAD system (in this example: Rhinoceros 5.0). This video showcases how an initial model consisting of two squares drawn in two alternative ways can be queried and restructured in a number of different arrangements of closed polygons under isometric transformations. The first example shows how a pictorial query of a spatial relation between two root2 triangles sharing a vertex and have their respective hypotenuses embedded in a single line yields four distinct instances in the initial shape. The second example how a pictorial query of two root2 triangles having their hypotenuses parallel to each other and reflected along the leading diagonal of the underlying square yields two instances in the shape. Note that the shape machine can calculate the symmetries of the matches and give the correct number of non-equivalent instances. The second part of the video ends up with a query of spatial relation of three root2 triangles.

The third part of the video shows how Shape Machine is able to access any type of a polyline within a shape without caring whether the boundaries of the polylines are registered or not in the database of a CAD system (in this example: Rhinoceros 5.0). This video showcases a series of queries starting from arrangements of polylines in the form of letters of the alphabet, including As, Ms, and Ks whose boundaries and intersections are found in the underlying structure of the square. These queries yield four instances for each arrangement of polylines. The video continues with queries for polylines whose boundaries are not in the structure of the queried shape using al lower-case k and a smaller version of the lower-case k to yield respectively 8 instances for each search. Note that one boundary of the initial lower-case k and three boundaries of the smaller version of the lower-case k are not in the database of the CAD system. Note as well that the shape machine can calculate the symmetries of the matches and give the correct number of non-equivalent instances.

Find Polylines in a 5-Star Polygon

Tzu-Chieh Kurt Hong
02/09/2019

The first part of the video showcases how an initial model of a regular 5-star polygon can be queried and restructured in a series of different closed polygons under similarity transformations. The video starts with the query of an isosceles triangle whose pair of angles are coincident with the angles of the regular 5-star pentagon to show five matches under similarity transformations. The next examples show the searches for two types of quadrilaterals, one convex and one concave, that both yield five matches each; a regular pentagon that yields one match; and a concave heptagon that yields five matches again, all under similarity transformations. In all cases, the Shape Machine calculates the exact number of matches without any duplicates.

The second part of the video showcases how an initial model of a regular 5-star polygon can be queried and restructured in a series of different polylines and arrangements of three lines under similarity transformations. The video starts with the queries of three-line shapes whose boundaries and intersections can also be found in the underlying structure of the 5-star polygon. The first shape consists of a single three-line polyline; the second consists of an arrangement of two polylines, a two-line polyline and a single one; and the third consists of three floating lines. All queries yield ten results to match the intuition of finding ten asymmetric shapes within the structure of the five-fold dihedral symmetry of the 5-star polygon of order 10. The next series of queries repeat the types of shapes discussed above with the extra provision that one or more of their boundaries are not registered in the database of the CAD system. The final example shows the search of a shape consisting of three lines of various lengths irrelevant to the lengths of the edges of the underlying star-polygon in such a spatial arrangement that no line touches one another. This search identifies ten similar copies in the model under similarity transformations specified by the user.

The third part of the video showcases how an initial model of a regular 5-star polygon can be queried and restructured in a series of different arrangements of polylines under similarity transformations. The first two vignettes showcase the search of two arrangements of polylines, a four-line shape and a seven-line shape respectively, that both can interpreted as arrangements of closed polygons, the first as an arrangement of two triangles and the second as a arrangement of three triangles. The final example showcase the successful search of an arbitrary part of the 5-star polygon selected through a lasso operation to demonstrate the ability of the Shape Machine to find all matching copies under similarity transformations, while introducing the idea of a visual query based on fragmentary evidence rather than a constructive specification.

Find Arcs in a Trefoil

Tzu-Chieh Kurt Hong
02/10/2019

The first part of the video showcases how an initial model of a regular trefoil-like shape can be queried in terms of arcs and arrangements of arcs under similarity transformations. The video starts with the query of a lens or vesica piscis shape, a classic figure in Euclid - and Carlo Scarpa’s work for that matter- and continues with a query for concatenated pairs of lens shapes, producing in both occasions three matches under similarity transformations. Different queries for open non symmetric polyarcs and arrangements of polyarcs whose endpoints are found in the database of the six points of the original CAD model produce six instances for each query respectively because of the dihedral symmetry of order six of the underlying trefoil.

The second example in this video shows how Shape Machine is able to access any part of a arc of a shape even though the queried parts of the arc are not registered in the database of the CAD system (in this example: Rhinoceros 5.0) The video consists of a series of queries of three-arc shapes whose endpoints are progressively not registered in the underlying structure of the underlying 3-lens shape. The first shape consists of a single connected three-arc shape; the second consists of an arrangement of a joint two-arc and a floating one; and the third and fourth consist of three floating arcs. The first shape has one endpoint not registered in the database; the second has two endpoints not registered; the third has three endpoints and the fourth all six not registered. All queries yield six results to match the intuition of finding six asymmetric shapes within the structure of the three-fold dihedral symmetry of the 3-lens polygon of order 6.

The third part of the video shows how Shape Machine is able to access any part of an arc of a shape and their combinations even though the queried parts are not registered in the database of CAD system (in this example: Rhinoceros 5.0). The first vignettes showcase the search of arrangements of poly arcs and lens shapes in an increasing spatial complexity in terms of number of lines and spatial relations to one another and to the whole. The final example showcases the successful search of an arbitrary part of the trefoil shape selected through a lasso operation to demonstrate the ability of the Shape Machine to find all matching copies under similarity transformations. A visual proof of the search is given in the end by marching the source shape with the missing part of the target shape.

Find Arrangements of Polylines Under Affinities

Tzu-Chieh Kurt Hong
02/10/2019

This example shows how Shape Machine is able to make queries of shapes under affine transformations. While this ability is a straightforward extension of the matching algorithms of the Shape Machine to include affinity transformations, the results are often less intuitive for the novice designer because under these transformations the shapes that are found often look and feel different from the ones used for the query. The first series of vignettes illustrate the point clearly: A search for a root 2 isosceles triangle yields four right angle triangles while a search of a square yields a rectangle and a rhombus. The third vignette shows how a search of a pentagonal envelope shape produces two sets of pentagonal shapes of different proportions. The fourth vignette shows how a search of hexagon produces two enantiomorphic versions of elongated hexagons. The last vignette shows the power of the Shape Machine to find affine copies that are harder to spot by the novice designer.

The second part of the video shows a series of vignettes that showcases the expressive power of Shape Machine to find arrangements of polygons, polylines and their combinations under affine transformations. The first vignette shows how a search for a spatial relation between two root-2 isosceles triangles in two squares yields two spatial relations between two affine triangles in two parallelograms. The second vignette shows how a second spatial relation between two instances of two collinear root-2 triangles with one coincident vertex can produce four matchings split in two families of two. The next four vignettes showcase searches for open polylines resembling letters of the alphabet like “R”, “M”, “A” and a deformed “U”, including polylines whose endpoints are not registered in the database of the CAD system. The penultimate two vignettes are poignant because they showcase how expressive Shape Machine can be and how it can help designers find parts that otherwise might be left unnoticed: these two vignettes take on the spatial relations between two open L-shape polylines one against the other. The resulting eight matches are hard to spot even for an experienced designer! The last vignette showcases the power of Shape Machine in bookkeeping giving only the unique number of matches counting symmetry.

The third part of the video shows a series of vignettes that showcases the expressive power of Shape Machine to find matches of arrangements of indefinite polylines and their combinations under affine transformations. The first vignette shows that the search of an equilateral triangle under affine transformations produces four matches characterized by triangles with diverse proportions. The second vignette shows that the search of an open three-line polyline - or a triangle that has one edge incomplete - produces twenty-four matches because of the symmetry of the polyline of order 1 vs. the symmetry of the four underlying triangles each of order 6. The third vignette shows that the search of a shape consisting of an open two-line polyline or an L-shape and a floating line produces again 24 matches because of the symmetry of the arrangement of order 1 vs. the symmetry of order 6 of each the four underlying triangles. The fourth vignette shows that the search of a shape consisting of three lines exhibiting rotational symmetry of order 3 produces 8 matches because of the symmetry of the arrangement of order 3 vs. the symmetry of order 6 of each the four underlying triangles. Finally, the fifth vignette shows that the search of a shape consisting of three lines exhibiting three-fold dihedral symmetry produces 4 matches because of the symmetry of the arrangement of order 6 vs. the symmetry of order 6 of each the four underlying triangles.

Making Shape Rules

The first part of this video showcases the usage of shape rules in the Shape Machine to make a fractal design. The rules are represented in the classical shape grammar format with the two sides of the production system, LHS and RHS, the arrow (→) in-between and the two registration marks on either side of the middle arrow (→) to fix the spatial relation between them. The series of the vignettes in the video illustrate the repeated application of a ready-made rule with its LHS showing a Root-2 isosceles triangle and its RHS the same Root-2 isosceles triangle with an additional line connecting the leading vertex of the isosceles triangle with the midpoint of its opposite edge. Note that this design action can be described in a number of ways, for example, if an isometric or a similar instance of a Root-2 isosceles triangle shown in the LHS is found in a design, this shape could be substituted by the same isometric or similar instance respectively of the two smaller Root-2 isosceles triangles depicted in the RHS respectively. The series of vignettes showcases the parallel application of the rule in a design comprised of 4 triangles to produce a series of fractal-like designs comprised by 4 +8=12 triangles, 4+8+16=28 triangles, 4+8+16+32=60 triangles and 4+8+16+32+64=124 triangles respectively. The last part of the video showcases how the individual phases of the production of the design can be retrieved and presented automatically by the Shape Machine at any time during the computation.

The second part of the video showcases how the RHS of a shape rule can be edited in the Shape Machine. The rules are represented in the classical shape grammar format with the two sides of the production system, LHS and RHS, the arrow (→) in-between and the two registration marks on either side of the middle arrow (→) to fix the spatial relation between them. The first vignette demonstrates the design of a RHS in the form of a schema t → t(x), for x a Root2 isosceles triangle and t(x) a translated copy of the Root2 isosceles triangle. The second vignette shows the design of a more complex RHS in the form of a schema x > x - prt(x) + y, for x a Root2 isosceles triangle, prt(x) a part of the Root2 isosceles triangle that is erased, and y a new set of lines in some spatial arrangement with the left over part of the Root2 isosceles triangle. Clearly this last action can be described in a number of alternative ways (Economou and Kotsopoulos, 2014).

The third and last part of the video showcases how new shape rules can be defined in the Shape Machine. The rules are represented in the classical shape grammar format with the two sides of the production system, LHS and RHS, the arrow (→) in between and the two registration marks on either side of the middle arrow (→) to fix the spatial relation between them. The three simple vignettes demonstrate the full power of the seamless introduction of new rules in a design process and their incredible power in the visual command of the expressiveness of a design.

Specify and Modify an Iceray Checkerboard Tessellation

Heather Ligler
02/20/2019

The first part of the video shows an exact digital reproduction in Shape Machine of the first study of George Stiny’s 1976 ice-ray grammar. The conventions of that analog grammar including the specification of the initial labeled shape and the labeled rules are exactly the same with the ones used in this digital grammar. In this vignette, an initial 4x5 grid is labeled to study patterns with alternating reflections as shown on the right side of the screen. On the left side of the screen, the rule template is shown in red for the construction of shape rules in the software. The left-hand-side of the rule is already given as one of the labeled cells of the overall grid design. The designer constructs a design for the cell by first copying the underlying structure from the left to the right side of the template, using the registration marks to ensure a correct location. Then, a new design is drawn on top while deleting and decomposing the reference geometry. The rule is then applied to all of the cells globally to generate a design.

The second part of the video builds on the regular ice-ray lattice study to explore the periodic and regular structure of ornamental designs. Using the same process as in the first video of the series, a shape rule is drawn to generate a design applied to an initial 4x5 grid of labeled cells organized to study patterns with alternative reflections as shown on the right side of the screen. The left side of the screen is the design space for drawing rules with the template as shown in red, the right side of the screen is the space for applying them to automate a design. A parallel application of the initial shape rule modified by a new spatial motif in the RHS produces new and unexpected results.

The last part of the video continues the ice-ray tiling study to explore the periodic and regular structure of ornamental designs. Here, rather than designing and replacing the complete motif of each labeled tile, the designer creates a new shape rule from selected parts of the tile. This new unlabeled shape rule is applied in a parallel fashion to the complete design to produce a new design changing dramatically its visual articulation from a curvilinear one to a rectilinear one.

Specifying and Modifying a Celtic Knot

Tzu-Chieh Kurt Hong
02/20/2019

A simple shape grammar generating Celtic knots is presented producing spirals, step patterns and key patterns in the style. The first vignette in the series shows the construction of two rules in the grammar that can be used to generate the growth of the pattern from a single loop to an alternating loop horizontally and vertically. The shape rules apply to shapes composed of arcs and straight lines under isometry transformations. The second part of the video shows a construction of a Celtic know by following the recursive application of four shape rules in the grammar. The last part of the video shows how the knot can be untied on the spot by making two new shapes to untie the overlapping strands.

Mechanical Gear

Tzu-Chieh Kurt Hong
02/20/2019

The first part of the video shows a mechanical design application to generate a gear in the Shape Machine. Designing the shape rules is straightforward. The first shape rule draws an initial circle defining the outer radius of the gear. The second shape rule offsets a 24-gon to define the inner radius of the gear. The third shape rule subdivides the outer radius to specify twelve wedged parts. Finally, the fourth shape rule specifies the design of a tooth at the outer boundary of the wedge. The mechanical gear is generated by the serial application of shape rules 1–3 one at a time, and the parallel application of shape rule 4 to all twelve parts of the design.

Thie second part of the video shows the design of a drawing script to generate a mechanical gear in the Shape Machine. On the left, the template for the DrawScript mode of Shape Machine is shown with four shape rules to specify the design automation. When the visual program is run, the rules are applied sequentially to: 1) draw an initial circle defining the outer radius of the gear; 2) offset a second circle to define the inner radius of the gear; 3) subdivide the outer radius to specify twelve parts; and 4) generate teeth at each of the twelve parts. The selection of the complete visual program in the DrawScript mode produces a gear design illustrated on the right with twelve teeth. At any time during the design process the designer can intervene in the DrawScript mode to change a shape rule and create a variation of the design. Here, the last shape rule that specifies the end of the gear is slightly edited to substitute its straight end with an arc end to specify a second design variation.

The third part of the video shows the editing of a visual script to generate a mechanical gear in the Shape Machine. On the left, the template for the DrawScript mode of Shape Machine is shown with four shape rules to specify the design automation. When the visual program is run, the rules are applied sequentially to: 1) draw an initial circle defining the outer radius of the gear; 2) offset a second circle to define the inner radius of the gear; 3) subdivide the outer radius to specify twelve parts; and 4) generate teeth at each of the twelve parts. In this design workflow, the designer changes rule four in a drastic way. This time the subdivision of the part and the subsequent drawing of two teeth generates a new design of a gear with twenty-four teeth. A variation of this rule four is tried again to generate a new design of twenty-four extended teeth. A large number of gears is easily generated, each following the sequence of four rules visually programmed in the DrawScript mode.

Tugendhat Restructured

Tzu-Chieh Kurt Hong
02/20/2019

Have you ever imported a file and found the geometry difficult to work with? This video shows the search, download, and import of a plan file describing Mies van der Rohe’s Tugendhat house and its translation into a maximal geometry representation for lines and arcs. The model once transcribed into the maximal line representation can be used in a straightforward way for analysis and synthesis in any vector-based software.

The second part of the video shows the editing of the Mies van der Rohe’s Tugendhat house plan into a series of layers and objects that fit the interests of the designer looking at the plan. The model once transcribed into the maximal line representation can be used in a straightforward way for analysis and synthesis in any vector-based software. Here the columns and the doors of the plan are reclassified and edited by shape rules that are drawn on the spot to automatically pick them up and clarify the drafting conventions specifying their appearance.

The third part of the video continues the editing of the Mies van der Rohe’s Tugendhat house plan into a series of layers and objects selected by the designer and includes drafting processes that are not easily captured by classifications of ready-made architectural parts. Here the vignette shows how a corner detail can be selected ad hoc by the designer and inserted in a shape rule to specify how the interior lines within the wall detail can be cleaned and how this rule can be used to apply to all corresponding parts of the plan.

Portmino

Heather Ligler
02/20/2019

In this video, a nine square Portm-Ino is generated as an interpretation of John Portman’s compositional rules for the design of a house. Shape rules on the left side of the screen are applied sequentially to build up the design from the initial grid to a fully articulated plan. The production is shown step-by-step on the right side of the screen to visualize the process. At each step, a caption is shown under the design to describe what the shape rule does when applied in the design context. For the sake of clarity in the video, only the rules necessary for this sample design are shown. The resulting Portm-Ino design is one of the set of possible designs that can be generated with the same limited set of rules applied to a 3x3 or nine square grid. The project is named Portm-Ino to suggest how the house in Portman’s conception is a systematic, residential configuration of a mat building along the lines of Le Corbusier’s Dom-Ino framework.

In the second part of the video, a nine square Portm-Ino is generated as an interpretation of John Portman’s compositional rules for the design of a house. Shape rules on the left side of the screen are applied sequentially to build up the design from the initial grid to a fully articulated plan. The production is shown step-by-step on the right side of the screen to visualize the process. At each step, a caption is shown under the design to describe what the shape rule does when applied in the design context. For the sake of clarity in the video, only the rules necessary for this sample design are shown. The resulting Portm-Ino design is one of the set of possible designs that can be generated with the same limited set of rules applied to a 3x3 or nine square grid. The project is named Portm-Ino to suggest how the house in Portman’s conception is a systematic, residential configuration of a mat building along the lines of Le Corbusier’s Dom-Ino framework.

In this last part of the video, a nine square Portm-Ino is generated as an interpretation of John Portman’s compositional rules for the design of a house. Shape rules on the left side of the screen are applied sequentially to build up the design from the initial grid to a fully articulated plan. The production is shown step-by-step on the right side of the screen to visualize the process. At each step, a caption is shown under the design to describe what the shape rule does when applied in the design context. For the sake of clarity in the video, only the rules necessary for this sample design are shown. The resulting Portm-Ino design is one of the set of possible designs that can be generated with the same limited set of rules applied to a 3x3 or nine square grid. The project is named Portm-Ino to suggest how the house in Portman’s conception is a systematic, residential configuration of a mat building along the lines of Le Corbusier’s Dom-Ino framework.

Sorting Binary

Tzu-Chieh Kurt Hong
03/01/2019

Sorting is an important algorithmic operation in programming. This video is aiming to demonstrate that binary sorting can easily be done by applying a simple shape rule with Shape Machine. Instead of writing code to sort binary digits, Shape Machine allows users to visually program this logic by considering the symbols 0 and 1 as shapes drawn in the shape rules: 10 → 01 or 01 → 10. The first rule when applied multiple times over a string of shapes made up of 0s and 1 produces the so-called big-endian order consisting of all 0s to the left and 1s to the right. The second rule when applied multiple times over a string of shapes made up of 0s and 1s produces the so-called little-endian order consisting of all 1s to the left and all 0s to the right. This video is a proof that Turing machine can be covered by the shape grammar formalism.

Sorting Alphabets

Tzu-Chieh Kurt Hong
03/01/2019

In current computer structure alphabetical sorting relies on an encoding system that encodes every symbol (numbers, letters, etc) to a binary representation, for example, ASCII coding system. By comparing the values of binary codes, the computer is able to sort alphabets. For instance, the ASCII code of letter “a” is “01100001” (in HEX, 61), letter “b” is “01100010” (in HEX, 62) and letter “c” is “01100011” (in HEX, 63). Because 01100001 is smaller than 01100010 and 01100010 is smaller than 01100011, letters “a”, “b” and “c” can be sorted as “abc” or “cba” by ordering the values of the binary codes. However, this is not straightforward if a programmer wants to sort these letters in the order such as “acb“ or “cab”. The relationship among the binary representations of these three letters has to redefined for a new sorting order. This video shows that Shape Machine is able to sort letters visually by simply applying shape rules. Furthermore, if users want a different sorting order, they can easily change the shape rules to obtain it.

Sorting 2D Binary

Tzu-Chieh Kurt Hong
03/01/2019

This video is aiming to demonstrate that 2D binary sorting can easily be done by writing simple shape rules in the DrawScript mode in Shape Machine. Instead of writing code to sort binary digits, Shape Machine allows users to visually program this logic by considering the symbols 0 and 1 as shapes drawn in shape rules. The initial shape consists of a 4X4 binary matrix of 1s and 0s in a random order both vertically and horizontally. The first shape rule specifies the horizontal sorting: when this rule is applied, all 1s will go to right and all 0s will go to left (big-endian order). The second shape rule specifies the vertical sorting: when this rule is applied, all 1s will go down and all 0s will go up. If we apply the first rule multiple times, we will sort the 0s and 1s horizontally and if we apply the second rule multiple times, we will sort the 0s and 1s vertically. In the first example, all 1s will go to down-right corner. If we want to sort in different ways, we can easily swap the left-hand-side and right-hand side in alternative ways to sort the 1s and the 0s in the other corners of the matrix respectively.

Boolean Gates

Tzu-Chieh Kurt Hong
03/01/2019

This video demonstrates how Shape Machine can calculate the basic Boolean gates used in circuit design to build a computer. Here six different Boolean gates are implemented in the DrawScript mode within the Shape Machine and they are from top-left to right-bottom: INV, XOR, OR, AND, NAN” and NOR logic gates. The INV or NOT gate, the inverter gate, has a single input and a single output: if the input of the inverter is 1, the output is 0; if the input is 0, the output is 1. The XOR or Exclusive-OR gate is a two-input and a single output Boolean gate: If the two inputs of the gate are the same, for example, 0 and 0 or 1 and 1, the output will be 0; If the two inputs of the XOR gate are not the same, for example, 1 and 0 or 0 and 1, then the output will be 1. The OR gate has two inputs and one output: If one of the two inputs is 1, for example, 1 and 0, 0 and 1, or 1 and 1, then the output will be 1; If both the inputs are 0s, that is, 0 and 0, then the output will be 0. The AND gate has two inputs and one output: If one of the input is 0, for example, 0 and 1, 1 and 0, or 0 and 0, then the output will be 0; If both inputs are 1s, that is, 1 and 1, then the output will be 1. The NAND gate is an AND gate followed by an Inverter it has two inputs and one output: If one of the inputs is 0, for example, 0 and 1, 1 and 0, or 0 and 0, then the output will be 1. If both inputs are 1s, that is, 1 and 1, then the output will be 0. The NOR gate is an OR gate followed by an Inverter and it has two inputs and one output: If one of the two inputs is 1, for example, 1 and 0, 0 and 1, or 1 and 1, then the output will be 0; If both the inputs are 0s, that is, 0 and 0, then the output will be 1.

Unsigned Binary Adder

Tzu-Chieh Kurt Hong
03/01/2019

This video shows how an unsigned binary adder can be implemented in DrawScript mode in the Shape Machine. The complete set of symbolic operations is captured here as a shape grammar consisting of 16 shape rules using the shapes 0, 1, C and ___ to perform the calculation. The addition is done exactly like adding decimal numbers, except that here we have only two digits, 0 and 1. The shape rules calculate the addition of the binary numbers writing the results of any carry to the bottom row. For example, if the Shape Machine sees an 1 which is above another 1 and both above a line ____ , deletes them both, draws a 0 below the line ___ and puts a C shape below to the next digit as a “carry” symbol to be substituted later by one of the next shape rules. The final result can be up to 5 digits, because the result can be larger than the number 1111. The example here demonstrates the addition of the numbers 11 and 7 in binary, that is, 1011 and 0111. The Shape Machine executes the sequence of shape rules in DrawScript mode and calculates the result equal to 10010, that is, 18.

Visual Calculator

Tzu-Chieh Kurt Hong
03/01/2019

In this video, a single-digit adder is implemented to demonstrate that numerical calculation can be done visually. This adder requires 29 shape rules which accomplish three different main operations: a) translating numbers (1, 2, 3, …, 9) to numbers of 1s (1, 11, 111, …, 111111111), b) moving all the 1s together and c) translating number of 1s (1, 11, 111, …, 111111111) to numbers (1, 2, 3, …, 9, 10). The concept of addition, moving all the 1s together, is commonly used in digital environment. Shape Machine can process this operation visually with a simple shape rule which is demonstrated in another video example (Sorting Binary) to achieve an adder. This example is a proof that implementing a computer with shape grammar is very possible in theory. This may lead us to another question: Can we implement a visual computer and how different will it be?