Fractal Ridge Vs Ps5
Kayla Munl
Graphics in this set are all fractal art, made in Fractal Extreme, then imported into Adobe Photo Shop and worked with in various ways. I love to hear what different people see in the graphics, they are almost like Rorschach Ink Blots in that respect, everyone sees something different.
Ridged perlin noise is actually fairly easy to do - you just have to ABS() either the final heightmap or some subset of the noise layers (and then invert the resulting height map values, to make sure the ridge occurs at the high values).
However, no simple modification to a fractal noise algorithm will give you those details that appear to "flow downhill" (and make the terrain much more realistic and appealing). To achieve those, you will need to add some kind of erosion simulation, which is a much more complex beast (both algorithm-wise and CPU-wise).
For some information on that, I recommend these two papers (you can ignore the GPU part, the algorithms work fine on CPU, although in my experience the simulation will take a minute or so for a 1000x1000 px image):
It shows two COS(x) functions, one of which was modulated with an ABS function (I have added a small offset to make sure both lines are visible separately). Now imagine that the purple line is flipped vertically - you end up with two mountains with sharp ridges and a valley in between:)
In order to produce physically realistic ridges, modifying the noise function is, as the previous answer stated, probably not the best way to go. Instead, if you start off with your fractal surface, and apply a decent erosion function to it, you can create ridged mountains with physically realistic shapes fairly easily.
Essentially, if your goal is simply ridges, you can modify the thermal erosion equation to remove all deposition (i.e. do subtractive-only erosion). I'm including the C# code I use to erode a single point - it's fairly fast, and will erode my 4096x4096 test landscape with 250 iterations in around 10 seconds on my PC (albeit with some parallelisation over 12 cores).
The messing around with bits is just an efficient way of getting the 8 neighbouring points of the point being eroded - my representation uses a linear array, so the y-coordinates are pre-multiplied by the width of the landscape (yMul etc...). You can treat stride as 1 for the purposes of simplicity. The r2demon and bit shift is just a fast multiplication by 1/sqrt(2) for the corner points.
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While the heat flow solutions of all three models, PSM, GDH1 and CHABLIS have singularity at the zero age, the common explanation about the cause of singularity is due to discrepancy between boundary conditions at the ridge crest where both depth and age are zero19,20,40. A model assuming a non-uniform temperature distribution at the ridge crest as initial condition was proposed which yields predicted heat flow curves free of a singularity40. In that model it introduced a new parameter 1/m representing the proportion of the upper cooling part of lithosphere in which the temperature reduced from T1 to T0 at the surface. 1/m can also be reviewed as relative depth of heat source in respect to the total thickness of lithosphere. This thermal model allows one to estimate the depth of the cooling below ridge crest (excluding zero) from heat flow measurement. If 1/m approaches to zero or m to infinity, the predicted heat flow solution reduced to the same as obtained by PSM model. Since the mid-ridge is usually considered the place where the asthenosphere and lithosphere meet, the cooling depth at the ridge can be thought as close to zero, thus the solution with singularity at the zero age. In the current paper, we will show that the fractal density of seafloor around the ridge crest can also cause singularity which has never been accounted previously in heat flow modelling. The singularity affects the cooling model especially the solution valid in the young age seafloor. It will show that account of the effect of fractal density will reduce the divergence between observed heat flow and the predicted heat flow by cooling models.
Heat flows are from sites in the North Pacific (north of Equator) and Northwest Atlantic. The averaged data in 2-Myr bins are denoted by dots and the standard deviation about the mean is denoted by the envelope. Red curves denote the results fitted using the Parsons and Sclater model (PSM), a cooling half-space model (HS) and the GDHl plate model (after Stein and Stein8). The solid black curve denotes the fit derived from the model presented here.
The dots represent the measured data (from Stein and Stein25), the dashed line denotes the fitted curve obtained using the GDH1 model and the solid lines symbolize the fitted curves obtained using the presented model.
Since density is a fundamental physical parameter involved in the thermal models (PSM, GDH1 and CHABLIS) used for prediction of heat flow at the mid ocean ridges, we will first introduce a new definition of fractal density with nonlinear property which was ignored by the traditional dynamics systems. The principle of density was discovered by the Greek scientist Archimedes approximately 2000 years ago. Density has become a foundational property of mass and energy and a well-known physical concept with a variety of applications in nearly all fields of study. The density of material or energy is defined as its mass or energy per unit volume. Therefore, density often has units of mass over volume (e.g., g/cm3, kg/m3) or energy over volume (J/cm3, w/L3).
where ρ is the average density of an object, which becomes independent of the volume only if the density of the object is uniform. However, if the object has heterogeneous properties, the density must be calculated using the derivative of the mass over volume:
The above density exists only if the limit converges when the volume becomes infinitesimal. In this paper, we will demonstrate that the limit in Eq. (2) does not always converge for complex objects with fractal properties. A new concept of fractal density is defined here as the limit of the following relation (3) if there is a parameter α (a positive value) so that the following limit converges51,52:
where Hα is a fractal thermal density with units of J/mα, and, accordingly, the ordinary thermal density H should contain a component expressed as power-law relationship of scale ε. Given the new definition of fractal density and fractal heat density, the heat flow q expressed in units of volume can be rewritten
where k is the thermal diffusivity which has been treated as constant in the standard analytic model and as a function of temperature in numerical modeling66 and qα is the heat flow calculated based on the fractal heat density. Therefore, the ordinary heat flow can be treated as the average heat flow per unit volume, obeying the power-law relationship with the volume. This relation (11) indicates that the ordinary heat flow q should be modified by the term tackling the singularity of the fractal density.
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Purpose: The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics.
Methods: The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) from 10 readers (three board certified radiologists and seven Radiology residents), formed the corpus for this study. The fractal dimension of the readers' visual scanning pattern was computed with the Minkowski-Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined.
Results: Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the complexity of visual scanning pattern when screening for breast cancer. No higher order effects were found to be significant.
This document discusses using a sliced ridgelet transform for image denoising. It begins with an introduction to ridgelet transforms and their effectiveness for image denoising compared to wavelet transforms. It then describes the proposed method which computes ridgelet transforms on slices of the noisy image to denoise each slice. After applying an inverse ridgelet transform, a Wiener filter is used to further improve the results by reducing blurring while preserving edges. Experimental results show the adaptive Wiener filter produces better results than linear filtering for denoising while maintaining high-frequency image components like edges.Read less
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