How to resolve the algorithm Chaos game step by step in the BASIC programming language

Published on 12 May 2024 09:40 PM
#Basic

How to resolve the algorithm Chaos game step by step in the BASIC programming language

Table of Contents

Problem Statement

The Chaos Game is a method of generating the attractor of an iterated function system (IFS). One of the best-known and simplest examples creates a fractal, using a polygon and an initial point selected at random.

Play the Chaos Game using the corners of an equilateral triangle as the reference points.   Add a starting point at random (preferably inside the triangle).   Then add the next point halfway between the starting point and one of the reference points.   This reference point is chosen at random. After a sufficient number of iterations, the image of a Sierpinski Triangle should emerge.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Chaos game step by step in the BASIC programming language

Source code in the basic programming language

10 SCREEN 1
20 X = INT(RND(0) * 200)
30 Y = INT(RND(0) * 173)
40 FOR I=1 TO 20000
50 V = INT(RND(0) * 3) + 1
60 ON V GOTO 70,100,130
70 X = X/2
80 Y = Y/2
90 GOTO 150
100 X = 100 + (100-X)/2
110 Y = 173 - (173-Y)/2
120 GOTO 150
130 X = 200 - (200-X)/2
140 Y = Y/2
150 PSET X,Y,V
160 NEXT I


10 HGR2
20 X = INT(RND(1) * 200)
30 Y = INT(RND(1) * 173)
40 FOR I=1 TO 20000
50 V = INT(RND(1) * 3) + 1
60 ON V GOTO 70,100,130
70 X = X/2
80 Y = Y/2
90 GOTO 150
100 X = 100 + (100-X)/2
110 Y = 173 - (173-Y)/2
120 GOTO 150
130 X = 200 - (200-X)/2
140 Y = Y/2
150 HCOLOR=V+4
160 HPLOT X,Y
170 NEXT I


#Chaos game

ancho = 500 : alto = 300
x = Int(Rand * ancho)
y = Int(Rand * alto)

Clg
FastGraphics
Graphsize ancho , alto

For iteracion = 1 To 30000
	vertice = Int(Rand * 3) + 1
	Begin Case
		Case vertice = 1
			x = x / 2
			y = y / 2
			Color red
		Case vertice = 2
			x = (ancho/2) + ((ancho/2)-x) / 2
			y = alto - (alto-y) / 2
			Color green
		Case vertice = 3
			x = ancho - (ancho-x) / 2
			y = y / 2
			Color blue
	End Case
	#Pset (x,y),vertice
	Plot (x,y)
Next iteracion
Refresh
ImgSave "chaos_game.jpg", "jpg"
End

100 REM Chaos game
110 CLS
120 SCREEN 7    '320x200 EGA Color
130 X = INT(RND(1) * 200)
140 Y = INT(RND(1) * 173)
150 FOR I=1 TO 20000
160  V = INT(RND(1) * 3) + 1
170  ON V GOTO 180,210,240
180  X = X/2
190  Y = Y/2
200  GOTO 260
210  X = 100 + (100-X)/2
220  Y = 173 - (173-Y)/2
230  GOTO 260
240  X = 200 - (200-X)/2
250  Y = Y/2
260  PSET(X,Y),V
270 NEXT I
280 END


100 PROGRAM "ChaosGam.bas"
110 RANDOMIZE 
120 GRAPHICS HIRES 4
130 LET X=RND(800):LET Y=RND(600)
140 FOR I=1 TO 20000
150   LET VERTEX=RND(3)
160   SELECT CASE VERTEX
170   CASE 0
180     LET X=X/2
190     LET Y=Y/2
200   CASE 1
210     LET X=400+(400-X)/2
220     LET Y=600-(600-Y)/2
230   CASE 2
240     LET X=800-(800-X)/2
250     LET Y=Y/2
260   END SELECT 
270   SET INK VERTEX+1
280   PLOT X,Y
290 NEXT

10 mode 1:randomize time:defint a-z
20 x = 640 * rnd
30 y = 400 * rnd
40 for i=1 to 20000
50 v = rnd * 2 + 1
60 on v goto 70,100,130
70 x = x/2
80 y = y/2
90 goto 150
100 x = 320 + (320-x)/2
110 y = 400 - (400-y)/2
120 goto 150
130 x = 640 - (640-x)/2
140 y = y/2
150 plot x,y,v
160 next i

100 REM Chaos game
110 CLS
120 SCREEN 2
130 X = INT(RND(1) * 256)
140 Y = INT(RND(1) * 192)
150 FOR I=1 TO 20000
160  V = INT(RND(1) * 3) + 1
170  ON V GOTO 180,220,260
180  X = X/2
190  Y = Y/2
200  V = 8 'red
210  GOTO 290
220  X = 128 + (128-X)/2
230  Y = 192 - (192-Y)/2
240  V = 3 'green
250  GOTO 290
260  X = 256 - (256-X)/2
270  Y = Y/2
280  V = 7 'blue
290  PSET(X,Y),V
300 NEXT I
310 END


 10 LET X=RND*46
 20 LET Y=RND*40
 30 FOR I=1 TO 5000
 40 LET VERTEX=INT (RND*3)
 50 GOTO 60+VERTEX*30
 60 LET X=X/2
 70 LET Y=Y/2
 80 GOTO 140
 90 LET X=23+(23-X)/2
100 LET Y=40-(40-Y)/2
110 GOTO 140
120 LET X=46-(46-X)/2
130 LET Y=Y/2
140 PLOT X,42-Y
150 NEXT I


 10 LET x=RND*200
 20 LET y=RND*173
 30 FOR i=1 TO 20000
 40 LET vertex=INT (RND*3)
 50 IF vertex=1 THEN GO TO 100
 60 IF vertex=2 THEN GO TO 130
 70 LET x=x/2
 80 LET y=y/2
 90 GO TO 150
100 LET x=100+(100-x)/2
110 LET y=173-(173-y)/2
120 GO TO 150
130 LET x=200-(200-x)/2
140 LET y=y/2
150 INK vertex+1
160 PLOT x,y
170 NEXT i
180 INK 0

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