# Turk, Greg

Robert P. Munafo, 2023 Mar 30.

Greg Turk is a computer graphics researcher who is responsible for some of the first widely-published Mandelbrot images.

11 months before the better-known Scientific American article, the September 1984 issue of BYTE magazine had these images created by Greg Turk:

*The first Mandelbrot set images in a mainstream publication*

The final image shows the lambda-map equivalent of R2F(3/4B1)SF(2/3B*)

There are four views of a Mandelbrot image using the lambda map coordinate transform. Based on the BYTE article text, these images were probably created on a VAX 11/750 at West Coast University.

The same article also features an AppleSoft BASIC program written by Turk that plots Julia sets using the inverse-iteration method:

10 CX = 140:CY = 96 20 X = .50001:Y = 0 100 GOSUB 5000 110 HGR2 : HCOLOR= 3 120 FOR I = I TO 10: GOSUB 4000: NEXT 140 GOSUB 6000 160 GOSUB 4000 180 GOTO 140 999 END 1000 REM SQUARE ROOT OF X,Y 1001 REM ERROR CHECKS BY ROBERT MUNAFO 1005 T = Y 1010 S = SQR (X * X + Y * Y) 1020 IF X > S THEN Y = 0: GOTO 1030 1025 Y = SQR (( - X + S) / 2) 1030 IF X + S < 0 THEN X = 0: GOTO 1040 1035 X = SQR ((X + S) / 2) 1040 IF T < 0 THEN X = - X 1050 RETURN 2000 REM FOUR OVER L 2010 S = LX * LX + LY * LY 2020 LX = 4 * LX / S 2030 LY = - 4 * LY / S 2040 RETURN 3000 REM X,Y TIMES L 3010 TX = X:TY = Y 3020 X = TX * LX - TY * LY 3030 Y = TX * LY + TY * LX 3040 RETURN 4000 REM FUNCTION OF X,Y 4010 GOSUB 3000 4020 X = 1 - X 4030 GOSUB 1000 4040 IF RND (1) < .5 THEN X = -X:Y = -Y 4050 X = 1 - X 4060 X = X / 2:Y = Y / 2 4070 RETURN 5000 REM GET VALUES 5010 TEXT : HOME 5020 INPUT "WHAT IS LAMBDA? (X,Y) ";LX,LY 5030 GOSUB 2000 5040 INPUT "WHAT IS SCALE? ";SC 5050 SC = 2 * CX / SC 5060 RETURN 6000 REM PLOT X,Y 6010 HPLOT SC * (X - .5) + CX,CY - SC * Y 6020 RETURN

Here are some images created by the program (enhanced slightly by displaying the lambda value on screen with my HRCG):

lambda=(3,0) (San Marco dragon) |
lambda=(0,1) |

lambda=(1,0) |
lambda=(-0.7406,1.186) |

As of 1996, Greg Turk is professor at Georgia Tech.

revisions: 20110730 oldest on record; 20120131 link to HRCG; 20230330 change picture caption and give R2-name

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Apr 18. s.27