Turtle Graphics Research Articles

Turtle walk through functional language

In this paper implementation and usage of a turtle graphics in (pure) functional programming language - LispKit Lisp is described. With all basic graphics functions available, implementation of a turtle graphics is enabled. Since turtle graphics is second most common way of using graphics, this implementation is a significant improvement of LispKit Lisp abilities. All necessary functions of a turtle graphics are implemented in LispKit Lisp, and they simply should be appended to any program which uses them.

A non-Euclidean implementation of LOGO

This paper describes an implementation of the LOGO Turtle Graphics programming environment in non-Euclidean geometry. Turtle graphics and non-Euclidean geometry are described briefly, and consideration is given to some of the details and problems of implementation. We describe the ways in which the LOGO language must be modified for a non-Euclidean environment, and the geometrical problems encountered during implementation.

Verbal Interaction and Problem-Solving within Computer-Assisted Cooperative Learning Groups

Verbal interaction and problem-solving behavior of small cooperative peer groups were observed while these groups worked on a computer-assisted (non-programming) problem-solving task. The purpose of the study was to identify problem-solving behaviors which relate to success within this context. Thirty-six fourth grade students were assigned to groups of three to form six groups of high and six of average academic ability. All groups used a nonprogramming version of Logo turtle graphics to reproduce a given line design on the computer screen. Results indicate that there was no relationship between success and ability, and that successful groups asked more task-related questions, spent more time on strategy, and reached higher levels of strategy elaboration than did unsuccessful groups. High ability groups made a greater number of long task statements than did average groups, bindings are discussed within the theoretical frameworks of social cognition and modeling. Instructional implications, including those for the development of computer-assisted learning materials for peer group problem solving, are also discussed.

Classes of polyhedra defined by jet graphics

The uniform polyhedra form a fascinating set of objects for display on graphics output devices. When animated on graphics screens they help in visualization of three-dimensional structures and in understanding the geometrical properties and relationships between the various polyhedra. However, the coordinates of the vertices of these objects—the Platonic solids, the Archimedean solids, the Johnson solids and the starred regular polyhedra—are mostly very difficult and tedious to determine algebraically. When the objective is simply to display these solids on a graphics screen, rather than explicit coordinate calculation, another approach can be adopted: the use of jet graphics software. Turtle graphics provides a compact method of describing and displaying the two-dimensional analogies of these solids, and this research investigated to what extent three-dimensional turtle graphics, also known as jet graphics, could describe and also display the regular three-dimensional polyhedra. A number of methods applicable to many of the solids were invented. In particular, methods were found that apply to the infinite classes of prisms and anti-prisms, pyramids and dipyramids, cupolas, bicupolas and gyrobicupolas as well as some starred versions of these polyhedra. A new class of polyhedra, the star antiprisms, are shown to be facially equilateral only for the case when the parallel faces correspond to pentagrams. A single iterative algorithm for the finite class of convex regular polyhedra was found. However, this method applies to all Platonic solids except the icosahedron, and generalizes the Petrie polygon rings to form new infinite classes of polyhedra such as Petrie-prisms. A recursive algorithm is described which correctly displays all regular polyhedra and is generalizable to semiregular and other classes of polyhedra.

The implementation of a simple turtle graphics package

The implementation of a simple turtle graphics package

Turtle Graphics and Mathematical Induction

Although induction is widely used in mathematics, it is a difficult concept to explain in the classroom. For students who have had little experience with inductive thinking, inductive proofs can appear somewhat arbitrary and unconvincing.

MATHSTUFF Logo Procedures: Bridging the Gap between Logo and School Geometry

Much enthusiasm has been generated about students' investigating and exploring the world of Logo's “turtle graphics” to learn geometry. This enthusiasm is easy to understand, since the computer screen in which the Logo turtle moves represents a small portion of a mathematical plane. As it is taught in middle and junior high school, geometry is essentially the study of such a plane and the objects that exist within it. So creating shapes with the turtle clearly involves geometric thought. However, the geometric ideas encountered in Logo are many times not covered in the standard curriculum; thus, integrating Logo activities with textbook topics can be difficult. This article will describe how teachers familiar with Logo can employ some special procedures (or programs) that allow students to explore and use traditional geometric topics within the context of the exciting environment of Logo.

Further dynamic modelling with LOGO

The article describes the use of turtle graphics in dynamic models to teach certain topics in physics. Turtle graphics can, first of all, produce output that is a real-time simulation of the behaviour of a real physical system. Using this output, the problems of interpreting graphs may be avoided. Turtle graphics can also deal with representations such as phase diagrams in physical optics. It can do this in a particularly useful way, since there is a HT (hide turtle) command that makes the turtle invisible. The results of the work done by such a turtle may be displayed without any display of the process. Finally, turtle graphics allow a novel treatment of vector algebra, so that problems involving a central force may be dealt with without the complication of an x-y cartesian coordinate system. Apart from being intuitively attractive, the method also illuminates the concept of angular momentum.

Implementing Logo in Middle Level Classrooms

Several versions of Logo are on the market. Since Apple microcomputers are so common in the schools, I will describe briefly the two versions available for Apple hardware, MIT Logo, and Apple Logo. MIT Logo is now marketed by Terrapin, Inc. and Krell Software. The two programs are nearly identical. Apple Logo was developed by Logo Computer Systems, Inc. and is distributed directly by Apple Computer. Both versions contain turtle graphics, offer list processing, and perform floating point arithmetic operations (e.g., FORWARD 2.5). The difference is a subtle one. Apple Logo was designed to stand alone. It is sealed from outside alterations and is therefore user-proof. For example, it will not permit you to save a file with a name that has already been used. MIT seems to be oriented toward the more advanced computer user who may desire to interface with assembly-language routines. There are many more detailed differences. See Lough (1983) for specifics. In general, Apple Logo seems more appropriate for the elementary school user. A word of caution is in order. Some companies advertise turtle-graphics programs. Generally these do not

Fractals with turtle graphics: a CS2 programming exercise for introducing recursion

This paper describes a programming exercise developed and used in CS2 classes to help introduce recursive programming. Providing a set of primitives which comprise a graphics system allows the students to focus on top down design and the nature of recursion, rather than on implementation details. The exercise entails drawing approximations of fractals by using the graphics primitives which are provided. The exercise was positively received by the students and provided a basis on which to discuss top down design and the desirability of hiding implementation details.

Reflective and Reflexive Approaches to Microcomputer Graphics: A Study Comparing Logo Turtle Graphics Programming and Paint Graphics Software in Teaching Art Concepts to Sixth Grade Students

Reflective and Reflexive Approaches to Microcomputer Graphics: A Study Comparing Logo Turtle Graphics Programming and Paint Graphics Software in Teaching Art Concepts to Sixth Grade Students

Learning LOGO: effects on learning BASIC and statistics

Abstract Two experiments were conducted to examine the effects of a period of training in the use of the turtle graphics aspects of LOGO on both attitudes towards computers and the learning of BASIC and statistics. A group of 15 subjects spent 10 hours learning LOGO. Their performance on subsequent learning of BASIC was significantly better than that of a control group, but no differences were found in attitudes towards computers or in the learning of statistics.

Developing thinking skills through the use of simple computer programming.

The computer education program at the Austine School for the Deaf (ASD), Brattleboro, Vermont, is in its second year. A one-semester course, "Introduction to Computers," is offered to junior high and senior high students. Teaching this course has enabled ASD to see how students' thinking skills can be expanded through the use of simple BASIC programming, Logo turtle graphics, and data processing using the PFS:FILE program. Some of the thinking skills are as follows: developing problem-solving skills to discover the most direct paths to reach goals, logical sequencing, analyzing, and classifying and organizing facts. Included are examples of student-created programs, student-expanded programs, and teacher-created or outside source programs that challenge and develop the students' thinking skills. No teacher has to be a computer expert to use these activities.

Microworlds: Options for Learning and Teaching Geometry

What is the least common multiple of 54 and 360? You probably came up with the answer in a few seconds or even sooner if you have worked with turtle graphics recently! In any case, if the first number was 254 instead of 54, most of us would reach for paper, pencil, and even a calculator. How do you draw the bisector of an angle? Most likely, you would first locate a straightedge and compass or protractor, depending on the context of the problem. For each of these questions, a natural first step is to select appropriate tools.