Home » Archimedes archive » Micro User » MU 1992-05.adf » PD » Fractal/!Fractal/Helptext
Fractal/!Fractal/Helptext
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
Tape/disk: | Home » Archimedes archive » Micro User » MU 1992-05.adf » PD |
Filename: | Fractal/!Fractal/Helptext |
Read OK: | ✔ |
File size: | 3AAC bytes |
Load address: | 0000 |
Exec address: | 0000 |
File contents
3d\0\Click to generate 3d Mandelbrots, Julia_Sets and some other functions. 3d\3\Controls how the image colours are translated into the 3d height. 3d\4\Click to use a logarithmic height mapping, accentuating low values. 3d\5\Click to use an inverse logarithmic height mapping, accentuating high values. 3d\6\Click to use a linear height mapping. 3d\9\Enter the minimum height value to remove low heights. 3d\13\Enter a maximum height value to clip high heights. 3d\17\Enter the ratio for translating colours into heights. Increasing by 1 doubles the height mapping. 3d\21\Shows the current rotation angle as in the tool window, which may be changed. This is used when in 3d plot mode and by most of the 3d functions. 3d\25\Shows the current elevation angle as in the tool window, which may be changed. This is used when in 3d plot mode and by the 3d functions. 3d\29\The number of previous points for redisplay when dynamically altering the 3d viewpoint in the Lorenz and Rossler functions. 3d\33\You must click here to enter the new 3d settings. 3d\-1\Various 3d controls. Click on OK to enter the new settings. Bar\-1\Welcome to !Fractal.|MClick Select to open the image window, or Adjust to open the full screen window. Also drop a sprite here (or on a window) to reload it, or a FracPal file to set the palette. Data\2\Click to input the data for the function. Data\5\Click to input the data and redraw the image. Data\8\Click to reset the zoom size to the default. Data\11\Click to reset the variables to their defaults. Data\14\The x coordinate of the bottom left corner. Data\16\The y coordinate of the bottom left corner. Data\18\The x range to be plotted. Smaller values display finer detail. Data\20\The y range to be plotted. Smaller values display finer detail. Data\-1\This window sets the variables for the current function. List\-1\The list of fractal functions with the current one highlighted. Click on a function to select it. Select the redraw tool to see the function's image. Opt\0\When on, X/Y Guessing speeds up Mandelbrots etc. at the expense of some loss of accuracy. Opt\1\Set on to display the Fractal tool window. Opt\2\When on the previous image is saved whenever you generate a new image, memory permitting. The previous image may then be quickly recalled from the Display menu. Turn off to save memory. Opt\5\Sets the screen mode when in full screen mode. Opt\9\Sets the display mode to the same as the image mode. Opt\10\Sets the display mode to a user set value. Opt\13\Enter the number of any 256 colour mode. This allows use of custom screen modes. Opt\14\When on the screen will be blanked when generating images. This can double performance when using multisync modes. Opt\15\When on forces the use of slow but very accurate floating point arithmetic for Mandelbrots and some other functions. Use to get perfect results. Opt\18\Click to make the settings permanent. Opt\21\Click to enter the settings. Opt\-1\This panel controls the main Fractal options. Press Ok to enter your settings. Save\-1\To save the file, enter its filename and then drag the file icon to a filer window or directly to another application window. Tool\0\Click Select to zoom in, Adjust to zoom out. A zoom box will appear, following the mouse. Press Select to decrease the box, Adjust to increase. Press Menu to start the re-draw. To cancel zoom mode, click here again. Tool\1\The redraw icon. Click to generate the function's image. To enter multi-tasking mode whilst plotting, press Adjust. Click the redraw icon again to stop plotting. Tool\2\Click to start colour cycling. Press Menu to stop. Pressing Select whilst cycling stops the display, whilst Adjust reverses the direction. Tool\3\Click to open the data edit window for the current function. Tool\4\Click to select the default palette. Use Adjust for its inverse. Tool\5\Click to select the external palette. Use Adjust for its inverse. Double click a FracPal file to load an external palette. To edit external palettes, use the !FracPal application. Tool\6\Click to select the RGB palette. Use Adjust for its inverse. Tool\7\Click to select the Logical palette. Use Adjust for its inverse. Tool\8\Click to select the Grey palette. Use Adjust for its inverse. Tool\9\Click to select the Blue palette. Use Adjust for its inverse. Tool\10\Click to select the Green palette. Use Adjust for its inverse. Tool\11\Click to select the Red palette. Use Adjust for its inverse. Tool\12\Click to select the Black And White palette. Use Adjust for its inverse. Tool\13\Click to select the Landscape palette. Use Adjust for its inverse. Tool\14\Click Select to increment the display colours by 1, and Adjust to decrement. Hold down the button for repeated action. Tool\15\Click Select to increment the display colours by 8, and Adjust to decrement. Hold down the button for repeated action. Tool\16\Shows the current angle of rotation for 3d images. Double click to rotate the current image. Tool\17\Click Select to increment the rotation angle by 15�, Adjust for 5�. Hold down to repeat. Use the 3d Options panel to precisely enter the rotation angle. Tool\18\Click Select to decrement the rotation angle by 15�, Adjust for 5�. Hold down to repeat. Use the 3d Options panel to precisely enter the rotation angle. Tool\19\Shows the current elevation for 3d images. Tool\20\Click Select to increment the elevation angle by 15�, Adjust for 5�. Hold down to repeat. Use the 3d Options panel to precisely enter the elevation angle. Tool\21\Click Select to decrement the elevation angle by 15�, Adjust for 5�. Hold down to repeat. Use the 3d Options panel to precisely enter the elevation angle. 3d_Plane\14\The x-scalar for converting the original image. Use values <1 to avoid clipping when viewing from the side. 3d_Plane\16\The y-scalar for converting the original image. Use values less than x Scalar to give a better sense of perspective. 3d_View\14\The perspective distance. Use lower values to enhance the vanishing point factor. This only operates when rotation=0�. Bifurcate\22\Initial population, in the range 0-1.0. Try different values to see the effect on the pattern. Bifurcate\24\Maximum plots per growth rate. Use higher values at higher zooms. Bifurcate\26\Minimum calculations before plotting. Use to remove extraneous lines. Fault\14\The number of faults to be made. Fault\16\The size of the fault shape in OS units. Fault\18\The maximum vertical movement of each fault. Fault\20\The seed for the random number used to generate the landscape. To redraw, set Fault->Random off. Fault1\-1\Select the sprite to use for Sprite mode faulting. Load your own sprite file by dropping it onto any of !Fractal's windows. Henon_Maps\22\Try small alterations to this value to see the effect. Henon_Maps\24\Try small alterations to this value to see the effect. IFS_2d1\2\Click to input the values. IFS_2d1\5\Click to input the values and redraw the image. IFS_2d1\8\Click to input the values and store them in the internal IFS data list. IFS_2d1\11\Click to restore the values from the internal data list. IFS_2d1\14\Click to copy the values to a new item in the data list. IFS_2d1\17\Click to delete the item from the data list. IFS_2d1\20\Enter a descriptive name. IFS_2d1\24\Click to go to the previous item. IFS_2d1\25\The current item number. IFS_2d1\28\Click to go to the next item. IFS_2d1\30\Enter the number of affine transformations to use. IFS_2d1\32\Enter the number of points to plot before stopping. IFS_2d1\33\Enter the values for transforming the x position. The new x=x*x_factor+y*y_factor+factor. IFS_2d1\34\Enter the values for transforming the y position. The new y=x*x_factor+y*y_factor+factor. IFS_2d1\35\Enter the probability for each affine transformation, the total for which must be 1. IFS_2d1\36\Shows the running probability so you can check the total equals 1. IFS_2d2\-1\The list of IFS definitions currently loaded with the current entry highlighted. Click on a name to select it. Entries may also be stepped through from the data entry panel. The entries may be saved from the Save menu entry. Julia_Set\22\The maximum number of iterations before escaping. Higher values take longer but show more detail, especially near the boundary. Julia_Set\24\The minimum number of iterations before plotting. This allows the removal of low iteration values. To just plot the interior, set Interior=Max Iter from the menu and Max and Min iter to the same value. Julia_Set\26\Change the value here to alter the Julia shape. Julia_Set\28\Change the value here to alter the Julia shape. L-System1\2\Click to input the values. L-System1\5\Click to input the values and redraw the image. L-System1\8\Click to input the values and store them in the internal data list. L-System1\11\Click to restore the values from the internal data list. L-System1\14\Click to copy the values to a new item in the data list. L-System1\17\Click to delete the item from the data list. L-System1\19\Enter a descriptive name. L-System1\23\Click to go to the previous item. L-System1\24\The current item number. L-System1\27\Click to go to the next item. L-System1\31\Click to decrease the number of iterations which will produce a simpler display. L-System1\32\The number of levels of string substitution before plotting. L-System1\35\Click to increase the number of iterations which will produce a more complex display. L-System1\37\Enter the number of turns to complete a circle. L-System1\40\Enter the initial rule, consisting of 1 or more rule or draw characters. L-System1\41\Each character may be substituted by rule and/or drawing characters. Standard draw characters are F=Draw forwards, f=Move forwards, +=Turn left, -=Turn right, |=Turn 180�, [=Stack position, ]=Unstack position. L-System1\60\Enter the letter to be subsituted. A rule character may be the same as a draw character. Characters are interpreted as rules until the plotting commences, when only draw characters are processed. L-System1\61\Enter the string to replace the letter, composed of further rule and/or draw characters. A rule may refer to itself multiple times - this creates the expanding detail effect. L-System2\-1\The list of L-System definitions currently loaded with the current entry highlighted. Click on a name to select it. Entries may also be stepped through from the data entry panel. The entries may be saved from the Save menu entry. Lorenz_Map\22\Enter a new starting value to alter the image shape. Lorenz_Map\24\Enter a new starting value to alter the image shape. Lorenz_Map\26\Enter a new starting value to alter the image shape. Lorenz_Map\28\Smaller step rates plot slower with more detail. Try 2e-2 when using the dynamic 3d facility. Lorenz_Map\30\Enter the maximum value for (a) when using random plotting. Lorenz_Map\32\Enter the maximum value for (b) when using random plotting. Lorenz_Map\34\Enter the maximum value for (c) when using random plotting. Mandelbrot\22\The maximum number of iterations before escaping. Higher values take longer but show more detail, especially near the boundary. Mandelbrot\24\The minimum number of iterations before plotting. This allows the removal of low iteration values. To just plot the interior, set Interior=Max Iter from the menu and Max and Min iter to the same value. Martin_Map\22\Enter a new starting value to alter the image shape. Martin_Map\24\Enter a new starting value to alter the image shape. Martin_Map\26\Enter a new starting value to alter the image shape. Martin_Map\28\Enter the maximum value for (a) when using random plotting. Martin_Map\30\Enter the maximum value for (b) when using random plotting. Martin_Map\32\Enter the maximum value for (c) when using random plotting. Midpoint\14\Enter higher values to increase the number of "hills". Midpoint\16\Enter a lower value to produce smoother images. Midpoint\18\The random number used to generate the image. To recreate an image (say with a new roughness), turn off the random plot from the Midpoint menu. Midpoint\20\Enter a value>0 to set the cut off value - points below this level will be coloured blue. Midpoint\22\Enter the colour number to be used as the sea. Use !FracPal to see what the colour numbers look like. Newton\22\The maximum number of iterations before escaping. Higher values take longer but show more detail, especially near the boundaries. Newton\24\The accuracy level. When the calculated root equals the actual root to within this accuracy, the point is coloured. Higher values take longer to calculate but show more detail at high magnifications. Pickover\22\Enter a new starting value to alter the image shape. Pickover\24\Enter a new starting value to alter the image shape. Pickover\26\Enter a new starting value to alter the image shape. Pickover\28\Enter a new starting value to alter the image shape. Pickover\30\Enter the maximum value for (a) when using random plotting. Pickover\32\Enter the maximum value for (b) when using random plotting. Pickover\34\Enter the maximum value for (c) when using random plotting. Pickover\36\Enter the maximum value for (d) when using random plotting. Popcorn\22\In Julia mode the iteration limit, otherwise the length of each 'string'. Popcorn\24\Higher values produce more exaggerated plots. Popcorn\26\0 gives maximum detail, higher values give rougher images but plot much quicker. Not used in Julia mode. Popcorn\28\The escape value when in Julia mode. Higher values produce more detail but take longer to compute. Popcorn\30\The multiplier in the SIN and TAN equations. Experiment with different values. Quaternion\22\The 2nd Quaternion real value. Quaternion\24\The 4th Quaternion real value. Quaternion\26\The 1st Quaternion constant. Quaternion\28\The 2nd Quaternion constant. Quaternion\30\The 3rd Quaternion constant. Quaternion\32\The 4th Quaternion constant. Quaternion\34\The maximum number of iterations before escaping. Higher values take longer but show more detail, especially near the boundaries. Riemann\14\The source image size in relation to the sphere size. Larger values will make the image stretch more towards the north pole. Riemann\16\The globe size as a fraction of the total image size. Smaller values reduce the distortion introduced by the mapping process. Riemann\18\The colour used to fill in black pixels. The colour numbers are as shown in the !FracPal utility. Rossler\22\Enter a new starting value to alter the image shape. Rossler\24\Enter a new starting value to alter the image shape. Rossler\26\Enter a new starting value to alter the image shape. Rossler\28\Smaller step rates plot slower with more detail. Try 2e-2 when using the dynamic 3d facility. Rossler\30\Enter the maximum value for (a) when using random plotting. Rossler\32\Enter the maximum value for (b) when using random plotting. Rossler\34\Enter the maximum value for (c) when using random plotting. Unity\22\The maximum number of iterations before escaping. Higher values take longer but show more detail. Unknown\14\The name of the external sprite on display. Eof
00000000 33 64 5c 30 5c 43 6c 69 63 6b 20 74 6f 20 67 65 |3d\0\Click to ge| 00000010 6e 65 72 61 74 65 20 33 64 20 4d 61 6e 64 65 6c |nerate 3d Mandel| 00000020 62 72 6f 74 73 2c 20 4a 75 6c 69 61 5f 53 65 74 |brots, Julia_Set| 00000030 73 20 61 6e 64 20 73 6f 6d 65 20 6f 74 68 65 72 |s and some other| 00000040 20 66 75 6e 63 74 69 6f 6e 73 2e 0a 33 64 5c 33 | functions..3d\3| 00000050 5c 43 6f 6e 74 72 6f 6c 73 20 68 6f 77 20 74 68 |\Controls how th| 00000060 65 20 69 6d 61 67 65 20 63 6f 6c 6f 75 72 73 20 |e image colours | 00000070 61 72 65 20 74 72 61 6e 73 6c 61 74 65 64 20 69 |are translated i| 00000080 6e 74 6f 20 74 68 65 20 33 64 20 68 65 69 67 68 |nto the 3d heigh| 00000090 74 2e 0a 33 64 5c 34 5c 43 6c 69 63 6b 20 74 6f |t..3d\4\Click to| 000000a0 20 75 73 65 20 61 20 6c 6f 67 61 72 69 74 68 6d | use a logarithm| 000000b0 69 63 20 68 65 69 67 68 74 20 6d 61 70 70 69 6e |ic height mappin| 000000c0 67 2c 20 61 63 63 65 6e 74 75 61 74 69 6e 67 20 |g, accentuating | 000000d0 6c 6f 77 20 76 61 6c 75 65 73 2e 0a 33 64 5c 35 |low values..3d\5| 000000e0 5c 43 6c 69 63 6b 20 74 6f 20 75 73 65 20 61 6e |\Click to use an| 000000f0 20 69 6e 76 65 72 73 65 20 6c 6f 67 61 72 69 74 | inverse logarit| 00000100 68 6d 69 63 20 68 65 69 67 68 74 20 6d 61 70 70 |hmic height mapp| 00000110 69 6e 67 2c 20 61 63 63 65 6e 74 75 61 74 69 6e |ing, accentuatin| 00000120 67 20 68 69 67 68 20 76 61 6c 75 65 73 2e 0a 33 |g high values..3| 00000130 64 5c 36 5c 43 6c 69 63 6b 20 74 6f 20 75 73 65 |d\6\Click to use| 00000140 20 61 20 6c 69 6e 65 61 72 20 68 65 69 67 68 74 | a linear height| 00000150 20 6d 61 70 70 69 6e 67 2e 0a 33 64 5c 39 5c 45 | mapping..3d\9\E| 00000160 6e 74 65 72 20 74 68 65 20 6d 69 6e 69 6d 75 6d |nter the minimum| 00000170 20 68 65 69 67 68 74 20 76 61 6c 75 65 20 74 6f | height value to| 00000180 20 72 65 6d 6f 76 65 20 6c 6f 77 20 68 65 69 67 | remove low heig| 00000190 68 74 73 2e 0a 33 64 5c 31 33 5c 45 6e 74 65 72 |hts..3d\13\Enter| 000001a0 20 61 20 6d 61 78 69 6d 75 6d 20 68 65 69 67 68 | a maximum heigh| 000001b0 74 20 76 61 6c 75 65 20 74 6f 20 63 6c 69 70 20 |t value to clip | 000001c0 68 69 67 68 20 68 65 69 67 68 74 73 2e 0a 33 64 |high heights..3d| 000001d0 5c 31 37 5c 45 6e 74 65 72 20 74 68 65 20 72 61 |\17\Enter the ra| 000001e0 74 69 6f 20 66 6f 72 20 74 72 61 6e 73 6c 61 74 |tio for translat| 000001f0 69 6e 67 20 63 6f 6c 6f 75 72 73 20 69 6e 74 6f |ing colours into| 00000200 20 68 65 69 67 68 74 73 2e 20 49 6e 63 72 65 61 | heights. Increa| 00000210 73 69 6e 67 20 62 79 20 31 20 64 6f 75 62 6c 65 |sing by 1 double| 00000220 73 20 74 68 65 20 68 65 69 67 68 74 20 6d 61 70 |s the height map| 00000230 70 69 6e 67 2e 0a 33 64 5c 32 31 5c 53 68 6f 77 |ping..3d\21\Show| 00000240 73 20 74 68 65 20 63 75 72 72 65 6e 74 20 72 6f |s the current ro| 00000250 74 61 74 69 6f 6e 20 61 6e 67 6c 65 20 61 73 20 |tation angle as | 00000260 69 6e 20 74 68 65 20 74 6f 6f 6c 20 77 69 6e 64 |in the tool wind| 00000270 6f 77 2c 20 77 68 69 63 68 20 6d 61 79 20 62 65 |ow, which may be| 00000280 20 63 68 61 6e 67 65 64 2e 20 54 68 69 73 20 69 | changed. This i| 00000290 73 20 75 73 65 64 20 77 68 65 6e 20 69 6e 20 33 |s used when in 3| 000002a0 64 20 70 6c 6f 74 20 6d 6f 64 65 20 61 6e 64 20 |d plot mode and | 000002b0 62 79 20 6d 6f 73 74 20 6f 66 20 74 68 65 20 33 |by most of the 3| 000002c0 64 20 66 75 6e 63 74 69 6f 6e 73 2e 0a 33 64 5c |d functions..3d\| 000002d0 32 35 5c 53 68 6f 77 73 20 74 68 65 20 63 75 72 |25\Shows the cur| 000002e0 72 65 6e 74 20 65 6c 65 76 61 74 69 6f 6e 20 61 |rent elevation a| 000002f0 6e 67 6c 65 20 61 73 20 69 6e 20 74 68 65 20 74 |ngle as in the t| 00000300 6f 6f 6c 20 77 69 6e 64 6f 77 2c 20 77 68 69 63 |ool window, whic| 00000310 68 20 6d 61 79 20 62 65 20 63 68 61 6e 67 65 64 |h may be changed| 00000320 2e 20 54 68 69 73 20 69 73 20 75 73 65 64 20 77 |. This is used w| 00000330 68 65 6e 20 69 6e 20 33 64 20 70 6c 6f 74 20 6d |hen in 3d plot m| 00000340 6f 64 65 20 61 6e 64 20 62 79 20 74 68 65 20 33 |ode and by the 3| 00000350 64 20 66 75 6e 63 74 69 6f 6e 73 2e 0a 33 64 5c |d functions..3d\| 00000360 32 39 5c 54 68 65 20 6e 75 6d 62 65 72 20 6f 66 |29\The number of| 00000370 20 70 72 65 76 69 6f 75 73 20 70 6f 69 6e 74 73 | previous points| 00000380 20 66 6f 72 20 72 65 64 69 73 70 6c 61 79 20 77 | for redisplay w| 00000390 68 65 6e 20 64 79 6e 61 6d 69 63 61 6c 6c 79 20 |hen dynamically | 000003a0 61 6c 74 65 72 69 6e 67 20 74 68 65 20 33 64 20 |altering the 3d | 000003b0 76 69 65 77 70 6f 69 6e 74 20 69 6e 20 74 68 65 |viewpoint in the| 000003c0 20 4c 6f 72 65 6e 7a 20 61 6e 64 20 52 6f 73 73 | Lorenz and Ross| 000003d0 6c 65 72 20 66 75 6e 63 74 69 6f 6e 73 2e 0a 33 |ler functions..3| 000003e0 64 5c 33 33 5c 59 6f 75 20 6d 75 73 74 20 63 6c |d\33\You must cl| 000003f0 69 63 6b 20 68 65 72 65 20 74 6f 20 65 6e 74 65 |ick here to ente| 00000400 72 20 74 68 65 20 6e 65 77 20 33 64 20 73 65 74 |r the new 3d set| 00000410 74 69 6e 67 73 2e 0a 33 64 5c 2d 31 5c 56 61 72 |tings..3d\-1\Var| 00000420 69 6f 75 73 20 33 64 20 63 6f 6e 74 72 6f 6c 73 |ious 3d controls| 00000430 2e 20 43 6c 69 63 6b 20 6f 6e 20 4f 4b 20 74 6f |. Click on OK to| 00000440 20 65 6e 74 65 72 20 74 68 65 20 6e 65 77 20 73 | enter the new s| 00000450 65 74 74 69 6e 67 73 2e 0a 42 61 72 5c 2d 31 5c |ettings..Bar\-1\| 00000460 57 65 6c 63 6f 6d 65 20 74 6f 20 21 46 72 61 63 |Welcome to !Frac| 00000470 74 61 6c 2e 7c 4d 43 6c 69 63 6b 20 53 65 6c 65 |tal.|MClick Sele| 00000480 63 74 20 74 6f 20 6f 70 65 6e 20 74 68 65 20 69 |ct to open the i| 00000490 6d 61 67 65 20 77 69 6e 64 6f 77 2c 20 6f 72 20 |mage window, or | 000004a0 41 64 6a 75 73 74 20 74 6f 20 6f 70 65 6e 20 74 |Adjust to open t| 000004b0 68 65 20 66 75 6c 6c 20 73 63 72 65 65 6e 20 77 |he full screen w| 000004c0 69 6e 64 6f 77 2e 20 41 6c 73 6f 20 64 72 6f 70 |indow. Also drop| 000004d0 20 61 20 73 70 72 69 74 65 20 68 65 72 65 20 28 | a sprite here (| 000004e0 6f 72 20 6f 6e 20 61 20 77 69 6e 64 6f 77 29 20 |or on a window) | 000004f0 74 6f 20 72 65 6c 6f 61 64 20 69 74 2c 20 6f 72 |to reload it, or| 00000500 20 61 20 46 72 61 63 50 61 6c 20 66 69 6c 65 20 | a FracPal file | 00000510 74 6f 20 73 65 74 20 74 68 65 20 70 61 6c 65 74 |to set the palet| 00000520 74 65 2e 0a 44 61 74 61 5c 32 5c 43 6c 69 63 6b |te..Data\2\Click| 00000530 20 74 6f 20 69 6e 70 75 74 20 74 68 65 20 64 61 | to input the da| 00000540 74 61 20 66 6f 72 20 74 68 65 20 66 75 6e 63 74 |ta for the funct| 00000550 69 6f 6e 2e 0a 44 61 74 61 5c 35 5c 43 6c 69 63 |ion..Data\5\Clic| 00000560 6b 20 74 6f 20 69 6e 70 75 74 20 74 68 65 20 64 |k to input the d| 00000570 61 74 61 20 61 6e 64 20 72 65 64 72 61 77 20 74 |ata and redraw t| 00000580 68 65 20 69 6d 61 67 65 2e 0a 44 61 74 61 5c 38 |he image..Data\8| 00000590 5c 43 6c 69 63 6b 20 74 6f 20 72 65 73 65 74 20 |\Click to reset | 000005a0 74 68 65 20 7a 6f 6f 6d 20 73 69 7a 65 20 74 6f |the zoom size to| 000005b0 20 74 68 65 20 64 65 66 61 75 6c 74 2e 0a 44 61 | the default..Da| 000005c0 74 61 5c 31 31 5c 43 6c 69 63 6b 20 74 6f 20 72 |ta\11\Click to r| 000005d0 65 73 65 74 20 74 68 65 20 76 61 72 69 61 62 6c |eset the variabl| 000005e0 65 73 20 74 6f 20 74 68 65 69 72 20 64 65 66 61 |es to their defa| 000005f0 75 6c 74 73 2e 0a 44 61 74 61 5c 31 34 5c 54 68 |ults..Data\14\Th| 00000600 65 20 78 20 63 6f 6f 72 64 69 6e 61 74 65 20 6f |e x coordinate o| 00000610 66 20 74 68 65 20 62 6f 74 74 6f 6d 20 6c 65 66 |f the bottom lef| 00000620 74 20 63 6f 72 6e 65 72 2e 0a 44 61 74 61 5c 31 |t corner..Data\1| 00000630 36 5c 54 68 65 20 79 20 63 6f 6f 72 64 69 6e 61 |6\The y coordina| 00000640 74 65 20 6f 66 20 74 68 65 20 62 6f 74 74 6f 6d |te of the bottom| 00000650 20 6c 65 66 74 20 63 6f 72 6e 65 72 2e 0a 44 61 | left corner..Da| 00000660 74 61 5c 31 38 5c 54 68 65 20 78 20 72 61 6e 67 |ta\18\The x rang| 00000670 65 20 74 6f 20 62 65 20 70 6c 6f 74 74 65 64 2e |e to be plotted.| 00000680 20 53 6d 61 6c 6c 65 72 20 76 61 6c 75 65 73 20 | Smaller values | 00000690 64 69 73 70 6c 61 79 20 66 69 6e 65 72 20 64 65 |display finer de| 000006a0 74 61 69 6c 2e 0a 44 61 74 61 5c 32 30 5c 54 68 |tail..Data\20\Th| 000006b0 65 20 79 20 72 61 6e 67 65 20 74 6f 20 62 65 20 |e y range to be | 000006c0 70 6c 6f 74 74 65 64 2e 20 53 6d 61 6c 6c 65 72 |plotted. Smaller| 000006d0 20 76 61 6c 75 65 73 20 64 69 73 70 6c 61 79 20 | values display | 000006e0 66 69 6e 65 72 20 64 65 74 61 69 6c 2e 0a 44 61 |finer detail..Da| 000006f0 74 61 5c 2d 31 5c 54 68 69 73 20 77 69 6e 64 6f |ta\-1\This windo| 00000700 77 20 73 65 74 73 20 74 68 65 20 76 61 72 69 61 |w sets the varia| 00000710 62 6c 65 73 20 66 6f 72 20 74 68 65 20 63 75 72 |bles for the cur| 00000720 72 65 6e 74 20 66 75 6e 63 74 69 6f 6e 2e 0a 4c |rent function..L| 00000730 69 73 74 5c 2d 31 5c 54 68 65 20 6c 69 73 74 20 |ist\-1\The list | 00000740 6f 66 20 66 72 61 63 74 61 6c 20 66 75 6e 63 74 |of fractal funct| 00000750 69 6f 6e 73 20 77 69 74 68 20 74 68 65 20 63 75 |ions with the cu| 00000760 72 72 65 6e 74 20 6f 6e 65 20 68 69 67 68 6c 69 |rrent one highli| 00000770 67 68 74 65 64 2e 20 43 6c 69 63 6b 20 6f 6e 20 |ghted. Click on | 00000780 61 20 66 75 6e 63 74 69 6f 6e 20 74 6f 20 73 65 |a function to se| 00000790 6c 65 63 74 20 69 74 2e 20 53 65 6c 65 63 74 20 |lect it. 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To| 00002e70 20 72 65 63 72 65 61 74 65 20 61 6e 20 69 6d 61 | recreate an ima| 00002e80 67 65 20 28 73 61 79 20 77 69 74 68 20 61 20 6e |ge (say with a n| 00002e90 65 77 20 72 6f 75 67 68 6e 65 73 73 29 2c 20 74 |ew roughness), t| 00002ea0 75 72 6e 20 6f 66 66 20 74 68 65 20 72 61 6e 64 |urn off the rand| 00002eb0 6f 6d 20 70 6c 6f 74 20 66 72 6f 6d 20 74 68 65 |om plot from the| 00002ec0 20 4d 69 64 70 6f 69 6e 74 20 6d 65 6e 75 2e 0a | Midpoint menu..| 00002ed0 4d 69 64 70 6f 69 6e 74 5c 32 30 5c 45 6e 74 65 |Midpoint\20\Ente| 00002ee0 72 20 61 20 76 61 6c 75 65 3e 30 20 74 6f 20 73 |r a value>0 to s| 00002ef0 65 74 20 74 68 65 20 63 75 74 20 6f 66 66 20 76 |et the cut off v| 00002f00 61 6c 75 65 20 2d 20 70 6f 69 6e 74 73 20 62 65 |alue - points be| 00002f10 6c 6f 77 20 74 68 69 73 20 6c 65 76 65 6c 20 77 |low this level w| 00002f20 69 6c 6c 20 62 65 20 63 6f 6c 6f 75 72 65 64 20 |ill be coloured | 00002f30 62 6c 75 65 2e 0a 4d 69 64 70 6f 69 6e 74 5c 32 |blue..Midpoint\2| 00002f40 32 5c 45 6e 74 65 72 20 74 68 65 20 63 6f 6c 6f |2\Enter the colo| 00002f50 75 72 20 6e 75 6d 62 65 72 20 74 6f 20 62 65 20 |ur number to be | 00002f60 75 73 65 64 20 61 73 20 74 68 65 20 73 65 61 2e |used as the sea.| 00002f70 20 55 73 65 20 21 46 72 61 63 50 61 6c 20 74 6f | Use !FracPal to| 00002f80 20 73 65 65 20 77 68 61 74 20 74 68 65 20 63 6f | see what the co| 00002f90 6c 6f 75 72 20 6e 75 6d 62 65 72 73 20 6c 6f 6f |lour numbers loo| 00002fa0 6b 20 6c 69 6b 65 2e 0a 4e 65 77 74 6f 6e 5c 32 |k like..Newton\2| 00002fb0 32 5c 54 68 65 20 6d 61 78 69 6d 75 6d 20 6e 75 |2\The maximum nu| 00002fc0 6d 62 65 72 20 6f 66 20 69 74 65 72 61 74 69 6f |mber of iteratio| 00002fd0 6e 73 20 62 65 66 6f 72 65 20 65 73 63 61 70 69 |ns before escapi| 00002fe0 6e 67 2e 20 48 69 67 68 65 72 20 76 61 6c 75 65 |ng. 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Higher values | 000030c0 74 61 6b 65 20 6c 6f 6e 67 65 72 20 74 6f 20 63 |take longer to c| 000030d0 61 6c 63 75 6c 61 74 65 20 62 75 74 20 73 68 6f |alculate but sho| 000030e0 77 20 6d 6f 72 65 20 64 65 74 61 69 6c 20 61 74 |w more detail at| 000030f0 20 68 69 67 68 20 6d 61 67 6e 69 66 69 63 61 74 | high magnificat| 00003100 69 6f 6e 73 2e 0a 50 69 63 6b 6f 76 65 72 5c 32 |ions..Pickover\2| 00003110 32 5c 45 6e 74 65 72 20 61 20 6e 65 77 20 73 74 |2\Enter a new st| 00003120 61 72 74 69 6e 67 20 76 61 6c 75 65 20 74 6f 20 |arting value to | 00003130 61 6c 74 65 72 20 74 68 65 20 69 6d 61 67 65 20 |alter the image | 00003140 73 68 61 70 65 2e 0a 50 69 63 6b 6f 76 65 72 5c |shape..Pickover\| 00003150 32 34 5c 45 6e 74 65 72 20 61 20 6e 65 77 20 73 |24\Enter a new s| 00003160 74 61 72 74 69 6e 67 20 76 61 6c 75 65 20 74 6f |tarting value to| 00003170 20 61 6c 74 65 72 20 74 68 65 20 69 6d 61 67 65 | alter the image| 00003180 20 73 68 61 70 65 2e 0a 50 69 63 6b 6f 76 65 72 | shape..Pickover| 00003190 5c 32 36 5c 45 6e 74 65 72 20 61 20 6e 65 77 20 |\26\Enter a new | 000031a0 73 74 61 72 74 69 6e 67 20 76 61 6c 75 65 20 74 |starting value t| 000031b0 6f 20 61 6c 74 65 72 20 74 68 65 20 69 6d 61 67 |o alter the imag| 000031c0 65 20 73 68 61 70 65 2e 0a 50 69 63 6b 6f 76 65 |e shape..Pickove| 000031d0 72 5c 32 38 5c 45 6e 74 65 72 20 61 20 6e 65 77 |r\28\Enter a new| 000031e0 20 73 74 61 72 74 69 6e 67 20 76 61 6c 75 65 20 | starting value | 000031f0 74 6f 20 61 6c 74 65 72 20 74 68 65 20 69 6d 61 |to alter the ima| 00003200 67 65 20 73 68 61 70 65 2e 0a 50 69 63 6b 6f 76 |ge shape..Pickov| 00003210 65 72 5c 33 30 5c 45 6e 74 65 72 20 74 68 65 20 |er\30\Enter the | 00003220 6d 61 78 69 6d 75 6d 20 76 61 6c 75 65 20 66 6f |maximum value fo| 00003230 72 20 28 61 29 20 77 68 65 6e 20 75 73 69 6e 67 |r (a) when using| 00003240 20 72 61 6e 64 6f 6d 20 70 6c 6f 74 74 69 6e 67 | random plotting| 00003250 2e 0a 50 69 63 6b 6f 76 65 72 5c 33 32 5c 45 6e |..Pickover\32\En| 00003260 74 65 72 20 74 68 65 20 6d 61 78 69 6d 75 6d 20 |ter the maximum | 00003270 76 61 6c 75 65 20 66 6f 72 20 28 62 29 20 77 68 |value for (b) wh| 00003280 65 6e 20 75 73 69 6e 67 20 72 61 6e 64 6f 6d 20 |en using random | 00003290 70 6c 6f 74 74 69 6e 67 2e 0a 50 69 63 6b 6f 76 |plotting..Pickov| 000032a0 65 72 5c 33 34 5c 45 6e 74 65 72 20 74 68 65 20 |er\34\Enter the | 000032b0 6d 61 78 69 6d 75 6d 20 76 61 6c 75 65 20 66 6f |maximum value fo| 000032c0 72 20 28 63 29 20 77 68 65 6e 20 75 73 69 6e 67 |r (c) when using| 000032d0 20 72 61 6e 64 6f 6d 20 70 6c 6f 74 74 69 6e 67 | random plotting| 000032e0 2e 0a 50 69 63 6b 6f 76 65 72 5c 33 36 5c 45 6e |..Pickover\36\En| 000032f0 74 65 72 20 74 68 65 20 6d 61 78 69 6d 75 6d 20 |ter the maximum | 00003300 76 61 6c 75 65 20 66 6f 72 20 28 64 29 20 77 68 |value for (d) wh| 00003310 65 6e 20 75 73 69 6e 67 20 72 61 6e 64 6f 6d 20 |en using random | 00003320 70 6c 6f 74 74 69 6e 67 2e 0a 50 6f 70 63 6f 72 |plotting..Popcor| 00003330 6e 5c 32 32 5c 49 6e 20 4a 75 6c 69 61 20 6d 6f |n\22\In Julia mo| 00003340 64 65 20 74 68 65 20 69 74 65 72 61 74 69 6f 6e |de the iteration| 00003350 20 6c 69 6d 69 74 2c 20 6f 74 68 65 72 77 69 73 | limit, otherwis| 00003360 65 20 74 68 65 20 6c 65 6e 67 74 68 20 6f 66 20 |e the length of | 00003370 65 61 63 68 20 27 73 74 72 69 6e 67 27 2e 0a 50 |each 'string'..P| 00003380 6f 70 63 6f 72 6e 5c 32 34 5c 48 69 67 68 65 72 |opcorn\24\Higher| 00003390 20 76 61 6c 75 65 73 20 70 72 6f 64 75 63 65 20 | values produce | 000033a0 6d 6f 72 65 20 65 78 61 67 67 65 72 61 74 65 64 |more exaggerated| 000033b0 20 70 6c 6f 74 73 2e 0a 50 6f 70 63 6f 72 6e 5c | plots..Popcorn\| 000033c0 32 36 5c 30 20 67 69 76 65 73 20 6d 61 78 69 6d |26\0 gives maxim| 000033d0 75 6d 20 64 65 74 61 69 6c 2c 20 68 69 67 68 65 |um detail, highe| 000033e0 72 20 76 61 6c 75 65 73 20 67 69 76 65 20 72 6f |r values give ro| 000033f0 75 67 68 65 72 20 69 6d 61 67 65 73 20 62 75 74 |ugher images but| 00003400 20 70 6c 6f 74 20 6d 75 63 68 20 71 75 69 63 6b | plot much quick| 00003410 65 72 2e 20 4e 6f 74 20 75 73 65 64 20 69 6e 20 |er. Not used in | 00003420 4a 75 6c 69 61 20 6d 6f 64 65 2e 0a 50 6f 70 63 |Julia mode..Popc| 00003430 6f 72 6e 5c 32 38 5c 54 68 65 20 65 73 63 61 70 |orn\28\The escap| 00003440 65 20 76 61 6c 75 65 20 77 68 65 6e 20 69 6e 20 |e value when in | 00003450 4a 75 6c 69 61 20 6d 6f 64 65 2e 20 48 69 67 68 |Julia mode. High| 00003460 65 72 20 76 61 6c 75 65 73 20 70 72 6f 64 75 63 |er values produc| 00003470 65 20 6d 6f 72 65 20 64 65 74 61 69 6c 20 62 75 |e more detail bu| 00003480 74 20 74 61 6b 65 20 6c 6f 6e 67 65 72 20 74 6f |t take longer to| 00003490 20 63 6f 6d 70 75 74 65 2e 0a 50 6f 70 63 6f 72 | compute..Popcor| 000034a0 6e 5c 33 30 5c 54 68 65 20 6d 75 6c 74 69 70 6c |n\30\The multipl| 000034b0 69 65 72 20 69 6e 20 74 68 65 20 53 49 4e 20 61 |ier in the SIN a| 000034c0 6e 64 20 54 41 4e 20 65 71 75 61 74 69 6f 6e 73 |nd TAN equations| 000034d0 2e 20 45 78 70 65 72 69 6d 65 6e 74 20 77 69 74 |. 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Higher| 00003640 20 76 61 6c 75 65 73 20 74 61 6b 65 20 6c 6f 6e | values take lon| 00003650 67 65 72 20 62 75 74 20 73 68 6f 77 20 6d 6f 72 |ger but show mor| 00003660 65 20 64 65 74 61 69 6c 2c 20 65 73 70 65 63 69 |e detail, especi| 00003670 61 6c 6c 79 20 6e 65 61 72 20 74 68 65 20 62 6f |ally near the bo| 00003680 75 6e 64 61 72 69 65 73 2e 0a 52 69 65 6d 61 6e |undaries..Rieman| 00003690 6e 5c 31 34 5c 54 68 65 20 73 6f 75 72 63 65 20 |n\14\The source | 000036a0 69 6d 61 67 65 20 73 69 7a 65 20 69 6e 20 72 65 |image size in re| 000036b0 6c 61 74 69 6f 6e 20 74 6f 20 74 68 65 20 73 70 |lation to the sp| 000036c0 68 65 72 65 20 73 69 7a 65 2e 20 4c 61 72 67 65 |here size. 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Try 2e-2 whe| 00003910 6e 20 75 73 69 6e 67 20 74 68 65 20 64 79 6e 61 |n using the dyna| 00003920 6d 69 63 20 33 64 20 66 61 63 69 6c 69 74 79 2e |mic 3d facility.| 00003930 0a 52 6f 73 73 6c 65 72 5c 33 30 5c 45 6e 74 65 |.Rossler\30\Ente| 00003940 72 20 74 68 65 20 6d 61 78 69 6d 75 6d 20 76 61 |r the maximum va| 00003950 6c 75 65 20 66 6f 72 20 28 61 29 20 77 68 65 6e |lue for (a) when| 00003960 20 75 73 69 6e 67 20 72 61 6e 64 6f 6d 20 70 6c | using random pl| 00003970 6f 74 74 69 6e 67 2e 0a 52 6f 73 73 6c 65 72 5c |otting..Rossler\| 00003980 33 32 5c 45 6e 74 65 72 20 74 68 65 20 6d 61 78 |32\Enter the max| 00003990 69 6d 75 6d 20 76 61 6c 75 65 20 66 6f 72 20 28 |imum value for (| 000039a0 62 29 20 77 68 65 6e 20 75 73 69 6e 67 20 72 61 |b) when using ra| 000039b0 6e 64 6f 6d 20 70 6c 6f 74 74 69 6e 67 2e 0a 52 |ndom plotting..R| 000039c0 6f 73 73 6c 65 72 5c 33 34 5c 45 6e 74 65 72 20 |ossler\34\Enter | 000039d0 74 68 65 20 6d 61 78 69 6d 75 6d 20 76 61 6c 75 |the maximum valu| 000039e0 65 20 66 6f 72 20 28 63 29 20 77 68 65 6e 20 75 |e for (c) when u| 000039f0 73 69 6e 67 20 72 61 6e 64 6f 6d 20 70 6c 6f 74 |sing random plot| 00003a00 74 69 6e 67 2e 0a 55 6e 69 74 79 5c 32 32 5c 54 |ting..Unity\22\T| 00003a10 68 65 20 6d 61 78 69 6d 75 6d 20 6e 75 6d 62 65 |he maximum numbe| 00003a20 72 20 6f 66 20 69 74 65 72 61 74 69 6f 6e 73 20 |r of iterations | 00003a30 62 65 66 6f 72 65 20 65 73 63 61 70 69 6e 67 2e |before escaping.| 00003a40 20 48 69 67 68 65 72 20 76 61 6c 75 65 73 20 74 | Higher values t| 00003a50 61 6b 65 20 6c 6f 6e 67 65 72 20 62 75 74 20 73 |ake longer but s| 00003a60 68 6f 77 20 6d 6f 72 65 20 64 65 74 61 69 6c 2e |how more detail.| 00003a70 0a 55 6e 6b 6e 6f 77 6e 5c 31 34 5c 54 68 65 20 |.Unknown\14\The | 00003a80 6e 61 6d 65 20 6f 66 20 74 68 65 20 65 78 74 65 |name of the exte| 00003a90 72 6e 61 6c 20 73 70 72 69 74 65 20 6f 6e 20 64 |rnal sprite on d| 00003aa0 69 73 70 6c 61 79 2e 0a 00 45 6f 66 |isplay...Eof| 00003aac