**The Best of Creative Computing Volume 1 (published 1976)**

With these basics of coding for the turtle, the games played with the real environment eariler can be replayed with a more abstract representation. It is possible to extend the basic games in many ways; the following is a list of variations that can be used to introduce additional concepts. We can demonstrate the isomorphism of the movement of the turtle from one square to another and that of an ant crawling along a wire as in figure 7. [image] Figure 7 The notion of the length of a path can be introduced by taking as one unit the advance from one square to the next and thus the length of the path is the number of arcs followed by the ant above. The notion of distance between two points can be introduced through the problem of finding the shortest path between two squares. One can count these shortest paths and can find the difference between squares on a grid for any case given (figure 8). [image] Figure 8 The notion of a hamiltonian path can be explored by finding the longest path without passing through the same square twice. There is also the question of whether one can pass through all of the squares by that means. The notion of transportation time can be studied by associating an elementary time with each elementary action. For example, forward may take four seconds, turning right - 3 seconds, and turning left - 2 seconds. Thus one can look for the most rapid paths. There can be a race between two or more turtles subject to the constraint that they do not simultaneously occupy the same square. One can add the possibility that the lettuce moves. This movement can be deterministic (that is to say, known in advance by the turtle) or random (a game of strategy). 188 The idea of a non-square network can be introduced. The turtle can move in a network of hexagonal mesh (which is equivalent to a triangular mesh for the ant) with three orders: forward - as above, right - meaning turn 60 degrees to the right, and left - which means turn to the left by 60 degrees, plus two variants (RR and LL permitted or not). Another possible variation of the networks is triangular for the turtle or hexagonal for the ant which do not permit the command FF (figure 9). [image] Conditional instructions can be introduced. The four tests of the real turtle to see if it is touching an obstacle in the front, left, right or rear can be adopted as TEST CLEAR TO FRONT (RIGHT, LEFT, or REAR). These can be adopted with the LOGO like TEST followed by IFTRUE or IFFALSE sort of structure or it can be more like other programming languages and use an IF .... THEN (action) type of format. Additional forms of tests can be invented, such as test whether the turtle can see its food (by looking straight ahead) or smell it. The latter sense can be considered either directional or not, and may be a function of distance from the target. The list of applications of turtle geometry is far from being limited. The choice of this theme in the elementary school permits many possibilities, and removing the requirement for computer equipment has made this approach attractive. In effect, each child thus establishes his program, executes it and analyzes it. Reference Papert, S. and Solomon, C. Twenty things to do with your computer. Educational Technology, 1972, 9(4), 39-42. [image] "Continued in their present patterns of fragmented unrelation, our school curricula will insure a citizenry unable to understand the cybernated world in which they live." Marshall McLuhan - 1964