The root mean square value of the heights (or of the differences from the mean plane which, however, always is the z = 0 plane). Button Like Current Image sets the RMS value to that of the current image.

The minimum and maximum spatial frequency. Increasing the minimum frequency leads to “flattening” of the image, i.e. to removal of large features. Decreasing the maximum frequency limits the sharpness of the features.

Enables the multiplication of the Fourier coefficients by a Gaussian function that in the real space corresponds to the convolution with a Gaussian.

Enables the multiplication of the Fourier coefficients by a function proportional to 1/(1 + k²T²)^3/4, where T is the autocorrelation length. So, the factor itself is not actually Lorentzian but it corresponds to Lorentzian one-dimensional power spectrum density which in turn corresponds to exponential autocorrelation function (see section Statistical Analysis for the discussion of autocorrelation functions). This factor decreases relatively slowly so the finite resolution plays usually a larger role than in the case of Gaussian.

The autocorrelation length of the Gaussian or Lorentzian factors (see section Statistical Analysis for the discussion of autocorrelation functions).

Enables multiplication of Fourier coefficients by factor proportional to 1/k^p, where k is the spatial frequency and p is the power. This permits to generate various fractal surfaces.

The power p.

The shape (type) of placed objects. At present the possibilities include half-spheres, boxes, various pyramids, bumps, spikes and a few more weird shapes. The difference between half-sphere and full sphere is in the height. The full sphere includes also the height of the lower half. The same applies to nuggets.

The lateral object size, usually the side of a containing square.

The ratio between the x and y dimensions of an object – with respect to some default proportions.

Changing the aspect ratio does not always imply mere geometrical scaling, e.g. objects called nuggets change between half-spheres and rods when the ratio is changed.

A quantity proportional to the height of the object, normally the height of the highest point.

Enabling Scales with size makes unperturbed heights to scale proportionally to the sizes of individual objects. Otherwise the height is independent on size. Proportional scaling is useful with non-zero size variance to keep the shape of all objects identical (as opposed to elongating and flattening them vertically). If all objects have the same size the option has no effect.

Button Like Current Image sets the height value to a value based on the RMS of the current image.

The shapes can be truncated at a certain height, enabling creation of truncated cones, pyramids, etc. The truncation height is given as a proportion to the total object height. Unity means the shape is not truncated, zero would mean complete removal of the object.

The average number of times an object covers a pixel on the image. Coverage value of 1 means the surface would be exactly once covered by the objects assuming that they covered it uniformly and did not overlap. Values larger than 1 mean more layers of objects – and slower image generation.

The direction in which the surface is changed by adding objects. Positive and negative modifications correspond forming hills and pits adding objects, respectively. Zero value of the parameter means hills and pits are chosen randomly. Positive values mean hills are more likely, while the maximum value 1 means only hills. The same holds for pits and negative values.

For columnarity of zero the local surface modification works as described in the introduction. For columnarity of one (the maximum), the objects are considered to have also a lower part, which is a perfect mirror of the (visible) upper part. Once the lower object part touches any point on the surface, it sticks to it. This determines the final height. The range of heights grows quckly in this case and the volume is rather porous (not representable with a height field, of course). Values between 0 and 1 mean the object height is interpolated between the two extremes.

When this option is enabled, at most one object may be placed on any pixel of the surface. Hence, they never overlap. The Coverage option then does not determine how many objects are actually placed, but only how many the generator tries. Once there is no free space remaning where an object of given size could be added, increasing the coverage has no effect (beside slowing down the generation).

The rotation of objects with respect to some base orientation, measured anticlockwise. The orientation can be also randomised using the corresponding Variance.

Radius of the spherical particles in real units. The height and lateral dimensions must be the same physical quantity so there is only one dimensional parameter.

Standard deviation of radius distribution (Gaussian).

How much of the surface would be covered if it was covered uniformly by the deposited particles. If the simulation is unable to place as many particles as requested, usually due to too short time, an error message is displayed.

Simulation length, measured in the number of iterations.

The shape (type) of placed objects. At present the possibilities include various elongated shapes.

Ellipsoid	Bar	Cylinder
Nugget	Hexagonal rod

The shapes can be elongated along the x axis (as controlled by Aspect ratio). Their dimension in the orthogonal direction is given by width. The cross section is symmetrical. Therefore, the width determines both the horizontal width and height.

The ratio between the x and y dimensions, in other words, the elongation. It is always at least unity; the shapes are never squashed along the x axis. The aspect ratio distribution can be thus noticeably asymmetrical when the nominal aspect ratio is around unity and the variation is large.

In general, this parameter influences how much the shapes tend to form columnar structures (porous, if topographical images could represent it). The default value of zero can be imagined as the lower part of the shape melting upon impact and filling the depression it has fallen into. Note that the volume balance is somewhat approximate and the height at which the object settles may be such that sharp spikes on the surface pierce through it.

The maximum columnarity (1) means that once any part of the shape touches the surface, it sticks to it. For smaller positive values the final height is interpolated between the two heights gien by the two approaches.

If columnarity is negative, the shape is rammed into the surface. For the minimum value (−1) it settles at the lowest height for which at least one point of its entire lower boundary would not be below the original surface. Again, for other negative values the final height is interpolated.

The distribution of the noise value. The possibilities include Gaussian, exponential, uniform, triangular and salt and pepper distributions.

The salt and pepper distribution works somewhat differently than is usual in computer graphics since the range of values is unbounded. It is a bimodal distribution consiting of two δ-functions. In other words, a constant (given by RMS) is added and/or subtracted from the pixel values.

The noise can be generated as symmetrical or one-sided. The mean value of the distribution of a symmetrical noise is zero, i.e. the mean value of data does not change when a symmetrical noise is added. One-sided noise only increases (if positive) or decreases (if negative) the data values.

Root mean square value of the noise distribution. More precisely, it is the RMS of the corresponding symmetrical distribution in the case the distribution is one-sided.

Density is the fraction of values modified. If it is 1 all pixels are modified. When it is smaller some are left intact.

Average number of defects per scan line, including any dead time (as determined by parameter Within line).

Fraction of the time to scan one line that corresponds to actual data acquisition. The rest of time is a dead time. Value 1 means there is no dead time, i.e. all steps occur within the image. Value 0 means the data acquisition time is negligible to the total line scan time, consequently, steps only occur between lines.

If steps can occur inside a scan line it determines the horizontal scanning direction (assuming the slow axis scan is from top to bottom). For left to right scanning the left part of the scan line is contiguous with the data above and the right part with data below. For right to left scanning it is the opposite. The two directions are illustrated in the descriptions of Block line correction which corrects similar artefacts.

For cumulative steps the random step value is always added to the current value offset; for non-cumulative steps the new value offset is directly equal to the random step value.

The fraction of the the image covered by defect if they did not overlap. Since the defect may overlap, coverage value of 1 does not mean the image is covered completely.

Scar length in pixels.

Variance of the scar length, see Objects for description of variances.

Average number of defects per scan line, including any dead time (as determined by parameter Within line).

Fraction of the time to scan one line that corresponds to actual data acquisition. The rest of time is a dead time. Value 1 means there is no dead time, i.e. all value changes occur within the image. Value 0 means the data acquisition time is negligible to the total line scan time, consequently, value changes only occur between lines.

If steps can occur inside a scan line it determines the horizontal scanning direction (assuming the slow axis scan is from top to bottom). For left to right scanning the left part of the scan line is contiguous with the data above and the right part with data below. For right to left scanning it is the opposite. The two directions are illustrated in the descriptions of Block line correction which corrects similar artefacts.

Mean duration of the defect, measured in image size. Value 1 means the mean duration will be the entire image scanning time. Small values mean the defects will mostly occupy just one scan line.

With zero offsets all scan lines are tilted around the middle. In other words, the central image column remains unperturbed. Increasing the dispersion of the offsets moves the pivot points randomly more and more to left or right.

Characteristic wavelength of the hum, measured in the image.

Small spread means the noise is very narrow-band and looks more or less like as a pure sine wave. Large values produce a wider spectrum with beats and more distorted profile.

The number of random sine wave components that are used to construct the hum in each scan line.

One-dimensional staircase pattern, formed by steps of constant width and height.

One-dimensional pattern, formed by double-sided steps (ridges) constant width and height.

Superellipse-shaped pattern formed by concentric steps of constant width and height.

Superellipse-shaped pattern formed by concentric double-sided steps (ridges) of constant width and height.

Radial pattern formed by alternating high and low wedges.

Two-dimensional regular arrangement of rectangular holes, possibly round.

Two-dimensional regular arrangement of symmetrical pillars of several possible shapes (circular, square or hexagonal).

Two-dimensional regular arrangement of steps of fixed width and height.

The rotation of the pattern with respect to some base orientation, measured anticlockwise.

The magnitude of the lateral deformation. It is a relative numerical quantity essentially determining how far the deformation can reach.

The characteristic size of the deformations. It describes not how far the features are moved but how sharply or slowly the deformation itself changes within the horizontal plane.

The average number of times a particle is generated above each surface pixel.

Local height increase occurring when the particle sticks to a pixel. Since the horizontal size of the particle is always one pixel the height is measured in pixels. A height of one pixel essentially means cubical particles, as far as growth is concerned. From the point of view of collision detection the particles are considered infinitely small.

Central inclination angle with which the particles are generated (angle of incidence). The value of zero means very small angles of incidence have the highest probability. Large values mean that the particles are more likely to impinge at large angles than at small angles. But for large direction variance, the distribution is still isotropic in the horizontal plane.

Central direction in the horizontal plane with which the particles are generated. Large variance means the distribution is isotropic in the horizontal plane; for small variances the growth is anisotopic.

Method for determination of the pixel the particle will finally stick to. Two options exist at this moment. Weak relaxation, in which only the two pixels just immediately before collision and after collision are considered and the particle sticks to the lower of them. In the case of strong relaxation, a 3×3 neighbourhood is considered in addition. The particle can move to a lower neighbour pixel with a certain probability before sticking permanently.

The average number of times a particle is generated above each surface pixel.

Local height increase occurring when the particle falls onto a pixel.

Quantity to display in the image. Displacement is the sum of the real parts. Amplitude is the absolute value of the complex wave. Phase is the phase angle of the complex wave.

The number of point sources the waves propagate from.

One of the wave forms described above.

Approximate amplitude (rms) of heights in the generated image. Note it differs from the amplitude of individual waves: the amplitude of heights in the generated image would grow with the square root of the number of waves in such case, whereas it in fact stays approxiately constant unless the amplitude changes.

Spatial frequency of the waves. It is relative to the image size, i.e. the value of 1.0 means wavelength equal to the lenght of the image side.

Locations of the point sources. Zero corresponds to the image centre. The positions are also measured in image sizes. Generally, at least one of the corresponding variances should be non-zero; otherwise all the point sources coincide (some interesting patterns can be still generated with varying frequency though).

Decay determines how quickly the waves are attenuated. The value is measured in inverse wavelengths and given as a decimal logarithm, indicated by the units log₁₀.

One iteration consists of four steps: A Monte Carlo update of u, a time step of solution of the differential equation for v, another Monte Carlo step and another differential euqation time step. The values of v shown correspond to the second update. The quantity shown as u is the average from the two values surrounding in time the corresponding value of v. Hence the images of u are three-valued, not two-valued.

Temperature determines the probability with which the two-state variable u can flip to the other value if it results in a configurations with higher energy or similar (flips that lower the energy a lot occur unconditonally). A larger temperature means less separation between the two u domains.

Strength with which the continuous variable biases the energy of each pixel. For large values the inhibitor has larger influence compared to the surface tension.

Coupling factor between u and v in the differential equation for v.

Bias in the differential equation for v towards larger or smaller values.

Time step in the differential equation corresponding to one Monte Carlo step. So this parameter determines the relative speed of the two processes.

Range of values of the created images.

One iteration correspond to each pair of neighbour cell positions being checked for possible swapping once. However, this only holds in probabilistic sense. Some positions can be checked multiple times in one iterations, others not at all.

The unitless temperature determines the probability with which cells can swap into less energetically preferred configuration, as described above. The initial temperature is the temperature at which the annealing begins.

The unitless temperature at which the simulation finishes.

Fraction of component C in the A–C mixture.

Range of values of the created images.

The output image can capture just the final state, or it can be calculated by averaging a certain number of states before the end given by this parameter.

The fraction of component B in the mixture. The remainder is divided among A and C according to Component fraction.

Difference of formation energies for components A and B, relative to the maximum value.

Difference of formation energies for components A and C, relative to the maximum value.

Difference of formation energies for components B and C, relative to the maximum value.

The number of time steps when solving the coupled PDEs. Usually the state more or less ceases to evolve after a certain number of iterations – which, however, varies wildly with the pattern type and its parameters.

The average number of times a particle falls onto any given pixel. Coverage value of 1 means the surface would be covered by a monolayer, assuming the particles cover it uniformly.

The average number particles falling onto any given pixel per simulation step. Smaller values of flux lead to larger structures as the particles diffuse for longer time before they meet another particle. The value is given as a decimal logarithm, indicated by the units log₁₀.

The height of one particle which gives the height of the steps in the resulting image.

The probability that a free particle will finally stick and stop moving when it touches another single particle. Probabilities that the particle will stick if it touches two or three particles increase progressively depending on this value. The sticking probability is always zero for a particle with no neighbours and always one for a particle with all four neighbours.

The probability a particle that has not stuck will move if it touches another particle. The probability for more touching particles decreases as a power of the single-particle probability. Particles without any neighbours can always move freely.

A particle that has fallen on the top of an already formed cluster can have reduced probability to descend to the lower layer due to so called Schwoebel barrier. If this parameter is 1 there is no such barrier, i.e. particles can descend freely. Conversely, probability 0 means particles can never descend to the lower layer. The value is given as a decimal logarithm, indicated by the units log₁₀.

The shape of profile across a fibre. Options Semi-circle, Triangle, Rectangle and Parabola are self-explanatory. Quadratic spline shape corresponds to the three-part piecewise quadratic function that is the basis function of quadratic B-spline.

The average number of times a fibre would be placed onto any given pixel. Coverage value of 1 means the surface would be exactly once covered by the fibres assuming that they covered it uniformly and did not overlap. Values larger than 1 mean more layers of fibres – and slower image generation. The value is approximate and the actual coverage depends somewhat on other parameters.

Fibre width in pixels. It has the usual Variance associated, which determines the difference between entire fibres. However, the width can also vary along a single fibre. This is controlled by the Along fibre option. High values of variation along the fibre can in combination with some other options (in particular high lengthwise deformation and height variation) result in very odd looking images and possibly artefacts.

A quantity proportional to the height of the fibre, normally the height of the highest point. Similarly to Width, it has two variances, between entire fibres and along each individual fibre.

Enabling Scales with width makes unperturbed heights to scale proportionally with fibre width. Otherwise the height is independent on size.

Button Like Current Image sets the height value to a value based on the RMS of the current image.

The fibres can be truncated at a certain height, enabling creation of profiles in the form of truncated semi-circles, parabolas, etc. The truncation height is given as a proportion to the total fibre height. Unity means the fibre is not truncated, zero would mean complete removal of the fibre.

The rotation of fibres, measured anticlockwise. Zero corresponds to the left-to-right orientation.

Density controls how frequently the fibre is deformed along its length. Low density means gradual deformation on a large scale, whereas high density means the fibre is deformed often, leading to wavy or curly shapes.

How much the fibre is deformed in the direction perpendicular to its main direction. Increasing this value makes the fibre wavy, but in a relatively regular manner.

How much points of the fibre are moved along its length. Increasing this value causes irregular kinks and loops (or even knots) to appear.

The base lattice type. The random lattice corresponds to completely randomly placed points. Other types correspond to regular organisations of points (square, hexagonal, triangular), well-known tilings (Cairo, snub square, Penrose) or surface reconstructions (silicon 7×7).

The average cell size. More precisely, this parameter describes the mean point density. It is equal to the side of the square if the same number of points was organised to a square lattice.

Amount to which the lattice is allowed to relax. The relaxation process pushes points away from very close neighbours and towards large empty space. The net result is that cell sizes become more uniform. Of course, relaxation has no effect on regular lattices. It should be noted that relaxation requires progressive retessellation and large relaxation parameter values can slow down the surface generation considerably.

Amount to which the random values assigned to each point (see below) are allowed to relax. The relaxation process is similar to diffusion and leads to overal smoothing of the random values.

The rotation of the lattice with respect to some base orientation, measured anticlockwise. It is only available for regular lattices as the random lattice is isotropic.

Parameters that control the lattice deformation. They have the same meaning as in Pattern synthesis.

Rounding interpolation between the random values assigned to each point of the set. This means each Voronoi cell is filled with a constant random value.

Linear interpolation between the random values assigned to each point of the set. Thus the surface is continuous, with each Delaunay triangle corresponding to a facet.

An interpolation similar to the previous one, but non-linear, creating relatively level areas around each point of the set.

Distance to the closest point of the set.

Distance to the closest Voronoi cell border, scaled in each cell segment so that the set point is in the same distance from all borders.

The same quantity as segmented distance, but multiplied by the radndom value assigned to the point of the set.

Distance to the closest Voronoi cell border.

The same quantity as border distance, but multiplied by the radndom value assigned to the point of the set.

Distance to the second nearest point of the set.

The design Hurst exponent H. For the normal values between 0 and 1, the square root of height-height correlation function grows as H-th power of the distance. The construction algorithm permits formally even negative values beause it stops at the finite resolution of one pixel.

Scale at which stationarity is enforced (note Fractional Brownian motion is not a stationary). When this scale is comparable to the image size or larger, it has little effect. However, when it is small the image becomes “homogeneised” instead of self-similar above this scale.

Distribution of the noise added during the generation. Uniform and Gaussian result in essentially the same surfaces (statistically); the former is faster though. More heavy-tailed distributions, i.e. exponential and especially power, lead to prominent peaks and valleys.

Power α for the power distribution. The probability density function is proportional to

The root mean square value of the heights (or of the differences from the mean plane which, however, always is the z = 0 plane). Note this value applies to the specific generated image, not the process as such, which does not have finite RMS. Button Like Current Image sets the RMS value to that of the current image.

Typical width of the stripe.

Spread of sizes (or, more precisely, spatial frequencies). Small spread means smooth regular features. However, for very small spread values preferred directions may appear in the image (it becomes anisotropic) due to the exhaustion of allowed spatial frequencies. Large spread means less regular phase boundaries and also more in-transition regions.

The difference between the values corresponding to the two phases, determining overall z-scale of the image.

Radius of the seed discs placed randomly at the beginnig.

The minimum allowed radius of all other discs. When there is no space for a disc of at least this size, the generation stop.

Additional separation from neighbour discs. While Minimum radius detemines the minimum size of the actually placed dics, this parameter increases the minimum size of free space allowing placement.

When enabled, all discs are expanded until they would touch their neighbours. The surface becomes tiles, with thin gaps between tiles.

Width of gaps between tiles after the tile transformation.

When enabled, the tiling is further post-processed using opening filter of given size. This removes too small tiles and makes the remaning ones rounder.

Size of the opening filter.

The height of discs or tiles with respect to the base, determining overall z-scale of the image. Heights of individual features will be spread around this value when Variance is non-zero.

The average number of particles per one pixel.

One iteration correspond to wind picking up randomly one particle in each pixel and deposting it elsewhere. However, the pixels are chosen randomly. Some locations may be chosen multiple times in one iteraton, others not at all. Some selected locations may also be bare bedrock with no sand particle to pick up.

The mean wind direction and wind direction spread. Small spread means the wind direction is consistent. Large values mean more random wind direction.

The sand particle can be imagined as only touching the surface occasionally and being carried by the wind high above it between. It can only be deposited when it touches the surface. The minimum step is the minimum distance (in pixels) of one such jump; the range gives the interval (again in pixels) from minimum to maximum jump length.

The probability the particle is deposited when it touches the bare bedrock.

The probability the particle is deposited when it touches the surface and there is already some sand. This probability should be generally higher than for bare rock.

When deposition of a particle (or picking up by wind) creates a too large height difference between neighbour pixels the sand becomes unstable. It then trickles down to either reduce the slopes of a hill for fill holes until the maximum slope is nowhere exceeded.

The approximate maximum radius of a plateau.

The approximate minimum radius of a plateau.

How fast the plateau size radius decreases with the increasing number of plateaus already there. High values mean the size decreases quickly and plateaus tend to be sparse and isolated. Low values mean the size decreases slowly and plateaus ten to be dense and stacked high.

How much the shapes can differ from symmetrical discs.

Approximate fraction of plateaus that overlap with another plateau.

The power with which plateau height scales with its radius. For the default power of 0 all pleateaus have the same height (apart from possible random spread). Positive powers mean the height decreases as the size decreased. Negative powers mean smaller plateaus are taller, creating a spiky surface.

The average number of times the liquid is propagated per pixel. The resulting image shows only the farthest points, so its average value is not in a simple relation to coverage.

The probability of random propagation from neighbour voxels, not according to the resistance based priority. Note that the value is logarithmic.