Example Mandelbrot plot

[krzysztof]

Hello everyone I am new here and it is my first post about Run BASIC. I don't want to start a new topic, so I decided to write in this one. I'd like to show You simple and short program for drawing Mandelbrot set (fractal).

'Mandelbrot set
graphic #Mandelbrot, 100, 100

for r1 = -2 to 2 step 0.04
 for r2 = -2 to 2 step 0.04

  x = 0
  y = 0

  for i = 1 to 100
   x1 = x * x - y * y + r1
   y = 2 * x * y + r2
   x = x1
   d = x * x + y * y
   if d > 4 then exit for
  next i

  #Mandelbrot color("white")
  #Mandelbrot set(25 * r1 + 50, 25 * r2 + 50)
  if d > 4 then #Mandelbrot color(0, 255 / i, 50 / i)
  #Mandelbrot set(25 * r1 + 50, 25 * r2 + 50)

 next r2
next r1

render #Mandelbrot
end

I wondered how fast it is, compared with other BASIC dialects. Similar program written in Free BASIC is very fast, but Free BASIC is compiler and differs in action. But one can compare speed of above program with other web-based BASIC dialect, for instance Quite BASIC www.quitebasic.com. Here is code for that interpreter:

10 REM Mandelbrot set
20 CLS
30 FOR R1 = -2 TO 2 STEP 0.04
40 FOR R2 = -2 TO 2 STEP 0.04
50 LET X = 0
60 LET Y = 0
70 LET J = 0
80 FOR I = 0 TO 100
90 LET X1 = X * X - Y * Y + R1
100 LET Y = 2 * X * Y + R2
110 LET X = X1
120 IF X * X + Y * Y > 4 THEN GOTO 150
130 NEXT I
140 LET J = 1
150 IF J = 0 THEN PLOT 25 * R1 + 50 , 25 * R2 + 50 , I
160 IF J = 1 THEN PLOT 25 * R1 + 50 , 25 * R2 + 50 , "BLACK"
170 NEXT R2
180 NEXT R1
190 END

The speed is very low!

[krzysztof]

This is a bit modified code that allows You to draw a larger picture of Mandelbrot set.

'Mandelbrot set
graphic #Mandelbrot, 200, 200

for i = 0 to 200
 for j = 0 to 200

  k = i / 80 - 1.75
  m = j / 80 - 1.25

  x = k
  y = m

  for n = 1 to 150
   x1 = x * x - y * y + k
   y = 2 * x * y + m
   d = x1 * x1 + y * y
   if d > 4 then exit for
   x = x1
  next n

  #Mandelbrot color("black")
  #Mandelbrot set(i, j)
  if d > 4 then #Mandelbrot color(1.7 * n, 255 / n, 50 / n)
  #Mandelbrot set(i, j)

 next j
next i
render #Mandelbrot
end

Increasing the size is limited because of error message "Your program has exceeded the allowable execution time". But with the current settings of the program, You should not receive this message.
For fun, try a a different palettes of colors, for example: color(n + 105, 1.7 * n, 0) or color(1.7 * n, 1.7 * n, 0).

[krzysztof]

In both programs You can enter a small improvement in the main loop. Termination of

for...to...
...
next

by the

exit for

is a little bit inelegant. This can be corrected in the very first program by placing a loop

while i <= 100 and d <= 4
...
i = i + 1
wend

It is necessary to insert

i = 1
d = 0

before this new loop! If You receive the color error when You start such modified program, change the expression

2.55 * i

to

2.5 * i

The second program for Mandelbrot set written in RunBASIC can be improved in the similar way.

[StefanPendl]

Aug 10, 2013 1:46:12 GMT -5 krzysztof said:

Increasing the size is limited because of error message "Your program has exceeded the allowable execution time".

You can overcome this by increasing the session timeout limit in the preferences.

[krzysztof]

Aug 11, 2013 1:18:24 GMT -5 StefanPendl said:

Aug 10, 2013 1:46:12 GMT -5 krzysztof said:

Increasing the size is limited because of error message "Your program has exceeded the allowable execution time".

You can overcome this by increasing the session timeout limit in the preferences.

Does not work in downloadable free version of RunBASIC.

[StefanPendl]

Sorry, it should have been the Runtime Timeout

[krzysztof]

Does not work, too. In the free version of RunBASIC, settings in the preferences are disabled. There is appropriate information: "Note: The following preferences can only be changed with the upgraded version of Run BASIC".

[StefanPendl]

It was a correction for those who are running the registered version and are therefore able to change the setting.