diff --git a/hc/src/help2.src b/hc/src/help2.src index a877b7b12..cc9e7aa9b 100644 --- a/hc/src/help2.src +++ b/hc/src/help2.src @@ -969,10 +969,10 @@ Select a fractal type: ; ~Topic=The Mandelbrot Set, Label=HT_MANDEL (type=mandel) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-mandel.png[link=help/images/type-mandel.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This set is the classic: the only one implemented in many plotting programs, and the source of most of the printed fractal images published. @@ -1056,10 +1056,10 @@ trust you. ; ~Topic=Julia Sets, Label=HT_JULIA (type=julia) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-julia.png[link=help/images/type-julia.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These sets were named for mathematician Gaston Julia, and can be generated by a simple change in the iteration process described for the @@ -1145,10 +1145,10 @@ matching Julia set. ~Topic=Inverse Julias, Label=HT_INVERSE_JULIA (type=julia_inverse) ; TODO: The thumbnail is so dark as to appear wholly black. -;~Doc-,Format- +;~Doc-,Format-,Online- ; ;image::help/images/thumbnails/type-julia_inverse.png[link=help/images/type-julia_inverse.png] -;~Doc+,Format+ +;~Doc+,Format+,Online+ Pick a function, such as the familiar Z(n) = Z(n-1) squared plus C (the defining function of the Mandelbrot Set). If you pick a point Z(0) @@ -1219,10 +1219,10 @@ corresponding Julia escape time fractal. ; ~Topic=Newton Domains of Attraction, Label=HT_NEWTON_BASINS (type=newtbasin) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-newtbasin.png[link=help/images/type-newtbasin.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The Newton formula is an algorithm used to find the roots of polynomial equations by successive "guesses" that converge on the correct value as @@ -1257,10 +1257,10 @@ See also: {Newton} ; ~Topic=Newton, Label=HT_NEWTON (type=newton) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-newton.png[link=help/images/type-newton.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The generating formula here is identical to that for {=HT_NEWTON_BASINS newtbasin}, but the @@ -1282,13 +1282,13 @@ Other values are 3 through 10. 8 has twice the symmetry and is faster. ; ~Topic=Complex Newton, Label=HT_NEWTON_COMPLEX (type=complexnewton, complexbasin) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-complexnewton.png[link=help/images/type-complexnewton.png] image:help/images/thumbnails/type-complexbasin.png[link=help/images/type-complexbasin.png] // -~Doc+,Format+ +~Doc+,Format+,Online+ Well, hey, "Z^n - 1" is so boring when you can use "Z^a - b" where "a" and "b" are complex numbers! The "complexnewton" and "complexbasin" @@ -1303,10 +1303,10 @@ there! ; ~Topic=Lambda Sets, Label=HT_LAMBDA (type=lambda) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-lambda.png[link=help/images/type-lambda.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This type calculates the Julia set of the formula lambda*Z*(1-Z). That is, the value Z[0] is initialized with the value corresponding to each pixel @@ -1326,10 +1326,10 @@ of fractals. ; ~Topic=Mandellambda Sets, Label=HT_MANDEL_LAMBDA (type=mandellambda) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-mandellambda.png[link=help/images/type-mandellambda.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This type is the "Mandelbrot equivalent" of the {=HT_LAMBDA lambda} set. A comment is @@ -1360,10 +1360,10 @@ for a way to experiment with different orbit intializations). ; ~Topic=Circle, Label=HT_CIRCLE (type=circle) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-circle.png[link=help/images/type-circle.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal types is from A. K. Dewdney's "Computer Recreations" column in "Scientific American". It is attributed to John Connett of the @@ -1386,10 +1386,10 @@ Id. This is because type circle and inside=startrail locks up Id. ; ~Topic=Plasma Clouds, Label=HT_PLASMA (type=plasma) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-plasma.png[link=help/images/type-plasma.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Plasma clouds are real live fractals, even though we didn't know it at first. They are generated by a recursive algorithm that randomly picks @@ -1450,10 +1450,10 @@ Saved plasma-cloud screens are excellent starting images for fractal ; ~Topic=Lambdafn, Label=HT_LAMBDA_FN (type=lambdafn) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-lambdafn.png[link=help/images/type-lambdafn.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Function=[sin|cos|sinh|cosh|exp|log|sqr|...]) is specified with this type. In the following description, we will use the shorthand "lambdasine" for @@ -1480,10 +1480,10 @@ floating-point code exclusively, use the float=yes parameter or the ; ~Topic=Halley, Label=HT_HALLEY (type=halley) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-halley.png[link=help/images/type-halley.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The Halley map is an algorithm used to find the roots of polynomial equations by successive "guesses" that converge on the correct value as @@ -1508,13 +1508,13 @@ whisker-like projections which generally point to a root. ; ~Topic=Phoenix, Label=HT_PHOENIX (type=phoenix, mandphoenix, phoenixcplx, mandphoenixclx) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-phoenix.png[link=help/images/type-phoenix.png] image:help/images/thumbnails/type-mandphoenix.png[link=help/images/type-mandphoenix.png] image:help/images/thumbnails/type-phoenixcplx.png[link=help/images/type-phoenixcplx.png] image:help/images/thumbnails/type-mandphoenixclx.png[link=help/images/type-mandphoenixclx.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The phoenix type defaults to the original phoenix curve discovered by Shigehiro Ushiki, "Phoenix", IEEE Transactions on Circuits and Systems, @@ -1544,13 +1544,13 @@ is an effective index to the phoenixcplx type. ; ~Topic=fn||fn Fractals, Label=HT_FN_OR_FN (type=lambda(fn||fn), manlam(fn||fn), julia(fn||fn), mandel(fn||fn)) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-lambda-fn-or-fn.png[link=help/images/type-lambda-fn-or-fn.png] image:help/images/thumbnails/type-manlam-fn-or-fn.png[link=help/images/type-manlam-fn-or-fn.png] image:help/images/thumbnails/type-julia-fn-or-fn.png[link=help/images/type-julia-fn-or-fn.png] image:help/images/thumbnails/type-mandel-fn-or-fn.png[link=help/images/type-mandel-fn-or-fn.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Two functions=[sin|cos|sinh|cosh|exp|log|sqr|...]) are specified with these types. The two functions are alternately used in the calculation @@ -1589,10 +1589,10 @@ julia set, julia(fn||fn). ; ~Topic=Mandelfn, Label=HT_MANDEL_FN (type=mandelfn) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-mandelfn.png[link=help/images/type-mandelfn.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Function=[sin|cos|sinh|cosh|exp|log|sqr|...]) is specified with this type. @@ -1614,7 +1614,7 @@ Peterson found them! ; ~Topic=Barnsley Mandelbrot/Julia Sets, Label=HT_BARNSLEY (type=barnsleym1, barnsleym2, barnsleym3, barnsleyj1, barnsleyj2, barnsleyj3) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-barnsleym1.png[link=help/images/type-barnsleym1.png] image:help/images/thumbnails/type-barnsleym2.png[link=help/images/type-barnsleym2.png] @@ -1623,7 +1623,7 @@ image:help/images/thumbnails/type-barnsleym3.png[link=help/images/type-barnsleym image:help/images/thumbnails/type-barnsleyj1.png[link=help/images/type-barnsleyj1.png] image:help/images/thumbnails/type-barnsleyj2.png[link=help/images/type-barnsleyj2.png] image:help/images/thumbnails/type-barnsleyj3.png[link=help/images/type-barnsleyj3.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Michael Barnsley has written a fascinating college-level text, "Fractals Everywhere", on fractal geometry and its graphic applications. (See @@ -1743,10 +1743,10 @@ overwritten each time a fractal is generated. ; ~Topic=Sierpinski Gasket, Label=HT_SIERPINSKI (type=sierpinski) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-sierpinski.png[link=help/images/type-sierpinski.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Another pre-Mandelbrot classic, this one found by W. Sierpinski around World War I. It is generated by dividing a triangle into four congruent @@ -1767,11 +1767,11 @@ integer math routines, so it runs fairly quickly. ; ~Topic=Quartic Mandelbrot/Julia, Label=HT_MANDEL_JULIA4 (type=mandel4, julia4) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-mandel4.png[link=help/images/type-mandel4.png] image:help/images/thumbnails/type-julia4.png[link=help/images/type-julia4.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractal types are the moral equivalent of the original M and J sets, except that they use the formula Z(n+1) = Z(n)^4 + C, which adds @@ -1788,10 +1788,10 @@ used this one only because we're lazy, and Z(n)^4 = (Z(n)^2)^2. ; ~Topic=Mandelbrot Mix 4, Label=HT_MANDELBROT_MIX4 (type=mandelbrotmix4) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-mandelbrotmix4.png[link=help/images/type-mandelbrotmix4.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Jim Muth published a "Fractal of the Day" on the Fractint mailing list for many years. As often as not Jim picks the formula @@ -1815,10 +1815,10 @@ requests the default bailout. ; ~Topic=DivideBrot5, Label=HT_DIVIDE_BROT5 (type=dividebrot5) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-dividebrot5.png[link=help/images/type-dividebrot5.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This is Jim Muth's fifth version of the DivideBrot formula. @@ -1835,7 +1835,7 @@ The formula is: ~Topic=Pickover Mandelbrot/Julia Types, Label=HT_PICKOVER_MANDEL_JULIA (type=manfn+zsqrd, julfn+zsqrd, manzpower, julzpower, manzzpwr, julzzpwr, manfn+exp, julfn+exp) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-manfn-plus-zsqrd.png[link=help/images/type-manfn-plus-zsqrd.png] image:help/images/thumbnails/type-manzpower.png[link=help/images/type-manzpower.png] @@ -1846,7 +1846,7 @@ image:help/images/thumbnails/type-julfn-plus-zsqrd.png[link=help/images/type-jul image:help/images/thumbnails/type-julzpower.png[link=help/images/type-julzpower.png] image:help/images/thumbnails/type-julzzpwr.png[link=help/images/type-julzzpwr.png] image:help/images/thumbnails/type-julfn-plus-exp.png[link=help/images/type-julfn-plus-exp.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These types have been explored by Clifford A. Pickover, of the IBM Thomas J. Watson Research center. As implemented in Id, they are regular @@ -1869,11 +1869,11 @@ to see a big biomorph digesting little biomorphs! ; ~Topic=Pickover Popcorn, Label=HT_POPCORN (type=popcorn, popcornjul) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-popcorn.png[link=help/images/type-popcorn.png] image:help/images/thumbnails/type-popcornjul.png[link=help/images/type-popcornjul.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Here is another Pickover idea. This one computes and plots the orbits of the dynamic system defined by: @@ -1902,10 +1902,10 @@ as to where the popcorn comes from. ; ~Topic=Dynamic System, Label=HT_DYNAMIC_SYSTEM (type=dynamic) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-dynamic.png[link=help/images/type-dynamic.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractals are based on a cyclic system of differential equations: x'(t) = -f(y(t))\ @@ -1944,10 +1944,10 @@ Pattern, Chaos, and Beauty". ; ~Topic=Mandelcloud, Label=HT_MANDEL_CLOUD (type=mandelcloud) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-mandelcloud.png[link=help/images/type-mandelcloud.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal computes the Mandelbrot function, but displays it differently. It starts with regularly spaced initial pixels and displays the resulting @@ -1965,7 +1965,7 @@ This fractal was invented by Noel Giffin. ~Topic=Peterson Variations, Label=HT_PETERSON_VARIATIONS (type=marksmandel, marksjulia, cmplxmarksmand, cmplxmarksjul, marksmandelpwr, tim's_error) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-marksmandel.png[link=help/images/type-marksmandel.png] image:help/images/thumbnails/type-marksjulia.png[link=help/images/type-marksjulia.png] @@ -1974,7 +1974,7 @@ image:help/images/thumbnails/type-cmplxmarksjul.png[link=help/images/type-cmplxm image:help/images/thumbnails/type-marksmandelpwr.png[link=help/images/type-marksmandelpwr.png] image:help/images/thumbnails/type-tims_error.png[link=help/images/type-tims_error.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractal types are contributions of Mark Peterson. MarksMandel and MarksJulia are two families of fractal types that are linked in the same @@ -1998,10 +1998,10 @@ created the type "tim's_error" after making an interesting coding mistake. ; ~Topic=Unity, Label=HT_UNITY (type=unity) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-unity.png[link=help/images/type-unity.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This Peterson variation began with curiosity about other "Newton-style" approximation processes. A simple one, @@ -2028,7 +2028,7 @@ let us know what you come up with! ~Topic=Scott Taylor / Lee Skinner Variations, Label=HT_TAYLOR_SKINNER_VARIATIONS (type=fn(z*z), fn*fn, fn*z+z, fn+fn, fn(z)+fn(pix), sqr(1/fn), sqr(fn), spider, tetrate, manowar) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-fn-zsqr.png[link=help/images/type-fn-zsqr.png] image:help/images/thumbnails/type-fn-mul-fn.png[link=help/images/type-fn-mul-fn.png] @@ -2044,7 +2044,7 @@ image:help/images/thumbnails/type-tetrate.png[link=help/images/type-tetrate.png] image:help/images/thumbnails/type-manowar.png[link=help/images/type-manowar.png] // -~Doc+,Format+ +~Doc+,Format+,Online+ Two of Id's faithful users went bonkers when we introduced the "formula" type, and came up with all kinds of variations on escape-time @@ -2068,12 +2068,12 @@ sin(z) - z^2 look very similar, but are different when you zoom in. ; ~Topic=Kam Torus, Label=HT_KAM (type=kamtorus, kamtorus3d) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-kamtorus.png[link=help/images/type-kamtorus.png] image:help/images/thumbnails/type-kamtorus3d.png[link=help/images/type-kamtorus3d.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This type is created by superimposing orbits generated by a set of equations, with a variable incremented each time. @@ -2110,7 +2110,7 @@ known as chaotic orbits! (Thanks, Wikipedia!) ; ~Topic=Bifurcation, Label=HT_BIFURCATION (type=bifurcation, bifmay, bifstewart, biflambda, bif=sinpi, bif+sinpi) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-bifurcation.png[link=help/images/type-bifurcation.png] image:help/images/thumbnails/type-bifmay.png[link=help/images/type-bifmay.png] @@ -2119,7 +2119,7 @@ image:help/images/thumbnails/type-bifstewart.png[link=help/images/type-bifstewar image:help/images/thumbnails/type-biflambda.png[link=help/images/type-biflambda.png] image:help/images/thumbnails/type-bif-eq-sinpi.png[link=help/images/type-bif-eq-sinpi.png] image:help/images/thumbnails/type-bif-plus-sinpi.png[link=help/images/type-bif-plus-sinpi.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The wonder of fractal geometry is that such complex forms can arise from such simple generating processes. A parallel surprise has emerged in the @@ -2247,11 +2247,11 @@ want to save it. ; ~Topic=Lorenz Attractors, Label=HT_LORENZ (type=lorenz, lorenz3d) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-lorenz.png[link=help/images/type-lorenz.png] image:help/images/thumbnails/type-lorenz3d.png[link=help/images/type-lorenz3d.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The "Lorenz attractor" is a "simple" set of three deterministic equations developed by Edward Lorenz while studying the non-repeatability of @@ -2317,10 +2317,10 @@ Try changing these a little at a time to see the result. ; ~Topic=Rossler Attractors, Label=HT_ROSSLER (type=rossler3d) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-rossler3d.png[link=help/images/type-rossler3d.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal is named after the German Otto Rossler, a non-practicing medical doctor who approached chaos with a bemusedly philosophical @@ -2341,10 +2341,10 @@ Default parameters are dt = .04, a = .2, b = .2, c = 5.7 ; ~Topic=Henon Attractors, Label=HT_HENON (type=henon) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-henon.png[link=help/images/type-henon.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Michel Henon was an astronomer at Nice observatory in southern France. He came to the subject of fractals via investigations of the orbits of @@ -2367,10 +2367,10 @@ The default parameters are a=1.4 and b=.3. ; ~Topic=Pickover Attractors, Label=HT_PICKOVER (type=pickover) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-pickover.png[link=help/images/type-pickover.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Clifford A. Pickover of the IBM Thomas J. Watson Research center is such a creative source for fractals that we attach his name to this one only with @@ -2388,10 +2388,10 @@ Default parameters are: a = 2.24, b = .43, c = -.65, d = -2.43 ; ~Topic=Gingerbreadman, Label=HT_GINGER (type=gingerbreadman) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-gingerbreadman.png[link=help/images/type-gingerbreadman.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This simple fractal is a charming example stolen from "Science of Fractal Images", p. 149. @@ -2404,11 +2404,11 @@ The initial x and y values are set by parameters, defaults x=-.1, y = 0. ; ~Topic=Martin Attractors, Label=HT_MARTIN (type=hopalong, martin) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-hopalong.png[link=help/images/type-hopalong.png] image:help/images/thumbnails/type-martin.png[link=help/images/type-martin.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractal types are from A. K. Dewdney's "Computer Recreations" column in "Scientific American". They are attributed to Barry Martin of Aston @@ -2435,11 +2435,11 @@ You will find three of these here: chip, quadruptwo, and threeply. ; ~Topic=Icon, Label=HT_ICON (type=icons, icons3d) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-icons.png[link=help/images/type-icons.png] image:help/images/thumbnails/type-icons3d.png[link=help/images/type-icons3d.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal type was inspired by the book "Symmetry in Chaos" by Michael Field and Martin Golubitsky (ISBN 0-19-853689-5, Oxford Press). @@ -2473,10 +2473,10 @@ There are 6 parameters: Lambda, Alpha, Beta, Gamma, Omega, and Degree ; ~Topic=Latoocarfian, Label=HT_LATOO (type=latoocarfian) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-latoocarfian.png[link=help/images/type-latoocarfian.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal type first appeared in the book "Chaos in Wonderland" by Clifford Pickover (ISBN 0-312-10743-9 St. Martin's Press). @@ -2496,11 +2496,11 @@ a > -3, b < 3, c > 0.5, d < 1.5 ; ~Topic=Quaternion, Label=HT_QUATERNION (type=quat,quatjul) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-quat.png[link=help/images/type-quat.png] image:help/images/thumbnails/type-quatjul.png[link=help/images/type-quatjul.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractals are based on quaternions. Quaternions are an extension of complex numbers, with 4 parts instead of 2. That is, a quaternion Q @@ -2534,11 +2534,11 @@ See also {HyperComplex} and {Quaternion and Hypercomplex Algebra} ; ~Topic=HyperComplex, Label=HT_HYPER_COMPLEX (type=hypercomplex,hypercomplexj) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-hypercomplex.png[link=help/images/type-hypercomplex.png] image:help/images/thumbnails/type-hypercomplexj.png[link=help/images/type-hypercomplexj.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractals are based on hypercomplex numbers, which like quaternions are a four dimensional generalization of complex numbers. It is not @@ -2567,10 +2567,10 @@ See also {Quaternion} and {Quaternion and Hypercomplex Algebra} ; ~Topic=Burning Ship, Label=HT_BURNING_SHIP (type=burning-ship) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-burning-ship.png[link=help/images/type-burning-ship.png] -~Doc+,Format+ +~Doc+,Format+,Online+ This fractal is a derivative of the classic Mandelbrot fractal with a twist. Some parts use absolute values in the equations and this gives an amazing @@ -2579,10 +2579,10 @@ angular quality to the fractal. ; ~Topic=Cellular Automata, Label=HT_CELLULAR (type=cellular) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-cellular.png[link=help/images/type-cellular.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractals are generated by 1-dimensional cellular automata. Consider a 1-dimensional line of cells, where each cell can have the value 0 or 1. @@ -3044,10 +3044,10 @@ For mathematical formulas of functions used in the parser language, see ; ~Topic=Frothy Basins, Label=HT_FROTH (type=frothybasin) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-frothybasin.png[link=help/images/type-frothybasin.png] -~Doc+,Format+ +~Doc+,Format+,Online+ Frothy basins, or riddled basins, were discovered by James C. Alexander of the University of Maryland. The discussion below is derived from a two page @@ -3106,10 +3106,10 @@ any shading. ; ~Topic=Julibrots, Label=HT_JULIBROT (type=julibrot) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-julibrot.png[link=help/images/type-julibrot.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The Julibrot fractal type uses a general-purpose renderer for visualizing three dimensional solid fractals. Originally Mark Peterson developed @@ -3182,10 +3182,10 @@ The screen dimensions provide the reference frame. ~Topic=Diffusion Limited Aggregation, Label=HT_DIFFUSION (type=diffusion) ; TODO: thumbnail appears almost completely black -;~Doc-,Format- +;~Doc-,Format-,Online- ; ;image::help/images/thumbnails/type-diffusion.png[link=help/images/type-diffusion.png] -;~Doc+,Format+ +;~Doc+,Format+,Online+ Standard diffusion begins with a single point in the center of the screen. Subsequent points move around randomly until coming into @@ -3234,10 +3234,10 @@ documentation. Juan J. Buhler added additional options. ; ~Topic=Lyapunov Fractals, Label=HT_LYAPUNOV (type=lyapunov) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-lyapunov.png[link=help/images/type-lyapunov.png] -~Doc+,Format+ +~Doc+,Format+,Online+ The bifurcation fractal illustrates what happens in a simple population model as the growth rate increases. The Lyapunov fractal expands that model @@ -3296,13 +3296,13 @@ A.K. Dewdney, Mathematical Recreations, Scientific American, Sept. 1991 ; ~Topic=Magnetic Fractals, Label=HT_MAGNET (type=magnet1m, magnet2m, magnet1j, magnet2j) -~Doc-,Format- +~Doc-,Format-,Online- image:help/images/thumbnails/type-magnet1m.png[link=help/images/type-magnet1m.png] image:help/images/thumbnails/type-magnet2m.png[link=help/images/type-magnet2m.png] image:help/images/thumbnails/type-magnet1j.png[link=help/images/type-magnet1j.png] image:help/images/thumbnails/type-magnet2j.png[link=help/images/type-magnet2j.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These fractals use formulae derived from the study of hierarchical lattices, in the context of magnetic renormalisation transformations. @@ -3374,10 +3374,10 @@ See {Finite Attractors} for more information on this aspect of Id internals. ; ~Topic=Volterra-Lotka Fractals, Label=HT_VOLTERRA_LOTKA (type=volterra-lotka) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-volterra-lotka.png[link=help/images/type-volterra-lotka.png] -~Doc+,Format+ +~Doc+,Format+,Online+ In the book "The Beauty of Fractals", these images are offered as an example of "how an apparently innocent system of differential equations @@ -3438,10 +3438,10 @@ Springer-Verlag, 1986; Section 8, pp. 125-7. ; ~Topic=Escher-Like Julia Sets, Label=HT_ESCHER (type=escher_julia) -~Doc-,Format- +~Doc-,Format-,Online- image::help/images/thumbnails/type-escher_julia.png[link=help/images/type-escher_julia.png] -~Doc+,Format+ +~Doc+,Format+,Online+ These unique variations on the Julia set theme, presented in "The Science of Fractal Images", challenge us to expand our pre-conceived notions of how